The Unreasonable Success of Local Search: Geometric Optimization

What is the effectiveness of local search algorithms for geometric problems in the plane? We prove that local search with neighborhoods of magnitude $1/\epsilon^c$ is an approximation scheme for the following problems in the Euclidian plane: TSP with random inputs, Steiner tree with random inputs, facility location (with worst case inputs), and bicriteria $k$-median (also with worst case inputs). The randomness assumption is necessary for TSP

On a Hopf operad containing the Poisson operad

A new Hopf operad Ram is introduced, which contains both the well-known Poisson operad and the Bessel operad introduced previously by the author. Besides, a structure of cooperad R is introduced on a collection of algebras given by generators and relations which have some similarity with the Arnold relations for the cohomology of the type A hyperplane arrangement. A map from the operad Ram to the dual operad of R is defined which we conjecture to be a isomorphism.Comment: Published by Algebraic and Geometric Topology at http://www.maths.warwick.ac.uk/agt/AGTVol3/agt-3-44.abs.htm

Energy-efficient algorithms for non-preemptive speed-scaling

We improve complexity bounds for energy-efficient speed scheduling problems for both the single processor and multi-processor cases. Energy conservation has become a major concern, so revisiting traditional scheduling problems to take into account the energy consumption has been part of the agenda of the scheduling community for the past few years. We consider the energy minimizing speed scaling problem introduced by Yao et al. where we wish to schedule a set of jobs, each with a release date, deadline and work volume, on a set of identical processors. The processors may change speed as a function of time and the energy they consume is the $\alpha$th power of its speed. The objective is then to find a feasible schedule which minimizes the total energy used. We show that in the setting with an arbitrary number of processors where all work volumes are equal, there is a $2(1+\varepsilon)(5(1+\varepsilon))^{\alpha -1}\tilde{B}_{\alpha}=O_{\alpha}(1)$ approximation algorithm, where $\tilde{B}_{\alpha}$ is the generalized Bell number. This is the first constant factor algorithm for this problem. This algorithm extends to general unequal processor-dependent work volumes, up to losing a factor of $(\frac{(1+r)r}{2})^{\alpha}$ in the approximation, where $r$ is the maximum ratio between two work volumes. We then show this latter problem is APX-hard, even in the special case when all release dates and deadlines are equal and $r$ is 4. In the single processor case, we introduce a new linear programming formulation of speed scaling and prove that its integrality gap is at most $12^{\alpha -1}$. As a corollary, we obtain a $(12(1+\varepsilon))^{\alpha -1}$ approximation algorithm where there is a single processor, improving on the previous best bound of $2^{\alpha-1}(1+\varepsilon)^{\alpha}\tilde{B}_{\alpha}$ when $\alpha \ge 25$

Effectiveness of Local Search for Geometric Optimization

What is the effectiveness of local search algorithms for geometric problems in the plane? We prove that local search with neighborhoods of magnitude 1/epsilon^c is an approximation scheme for the following problems in the Euclidean plane: TSP with random inputs, Steiner tree with random inputs, uniform facility location (with worst case inputs), and bicriteria k-median (also with worst case inputs). The randomness assumption is necessary for TSP

Spy-Game on Graphs

We define and study the following two-player game on a graph G. Let k in N^*. A set of k guards is occupying some vertices of G while one spy is standing at some node. At each turn, first the spy may move along at most s edges, where s in N^* is his speed. Then, each guard may move along one edge. The spy and the guards may occupy same vertices. The spy has to escape the surveillance of the guards, i.e., must reach a vertex at distance more than d in N (a predefined distance) from every guard. Can the spy win against k guards? Similarly, what is the minimum distance d such that k guards may ensure that at least one of them remains at distance at most d from the spy? This game generalizes two well-studied games: Cops and robber games (when s=1) and Eternal Dominating Set (when s is unbounded). We consider the computational complexity of the problem, showing that it is NP-hard and that it is PSPACE-hard in DAGs. Then, we establish tight tradeoffs between the number of guards and the required distance d when G is a path or a cycle. Our main result is that there exists beta>0 such that Omega(n^{1+beta}) guards are required to win in any n*n grid

Requirements for the selective degradation of CD4 receptor molecules by the human immunodeficiency virus type 1 Vpu protein in the endoplasmic reticulum

BACKGROUND: HIV-1 Vpu targets newly synthesized CD4 receptor for rapid degradation by a process reminiscent of endoplasmic reticulum (ER)-associated protein degradation (ERAD). Vpu is thought to act as an adaptor protein, connecting CD4 to the ubiquitin (Ub)-proteasome degradative system through an interaction with beta-TrCP, a component of the SCFbeta-TrCP E3 Ub ligase complex. RESULTS: Here, we provide direct evidence indicating that Vpu promotes trans-ubiquitination of CD4 through recruitment of SCFbeta-TrCP in human cells. To examine whether Ub conjugation occurs on the cytosolic tail of CD4, we substituted all four Ub acceptor lysine residues for arginines. Replacement of cytosolic lysine residues reduced but did not prevent Vpu-mediated CD4 degradation and ubiquitination, suggesting that Vpu-mediated CD4 degradation is not entirely dependent on the ubiquitination of cytosolic lysines and as such might also involve ubiquitination of other sites. Cell fractionation studies revealed that Vpu enhanced the levels of ubiquitinated forms of CD4 detected in association with not only the ER membrane but also the cytosol. Interestingly, significant amounts of membrane-associated ubiquitinated CD4 appeared to be fully dislocated since they could be recovered following sodium carbonate salt treatment. Finally, expression of a transdominant negative mutant of the AAA ATPase Cdc48/p97 involved in the extraction of ERAD substrates from the ER membrane inhibited Vpu-mediated CD4 degradation. CONCLUSION: Taken together, these results are consistent with a model whereby HIV-1 Vpu targets CD4 for degradation by an ERAD-like process involving most likely poly-ubiquitination of the CD4 cytosolic tail by SCFbeta-TrCP prior to dislocation of receptor molecules across the ER membrane by a process that depends on the AAA ATPase Cdc48/p97.This work was performed by JB in partial fulfillment of her doctoral thesis and was supported by grants from the Canadian Institutes of Health Research (CIHR) (MOP-14228) and from the Fonds de la Recherche en Santé du Québec (FRSQ) to EAC. JB is the recipient of a studentship from the FRSQ and EAC holds the Canada Research Chair in Human Retrovirology

Modulation of HIV-1-host interaction: role of the Vpu accessory protein

Viral protein U (Vpu) is a type 1 membrane-associated accessory protein that is unique to human immunodeficiency virus type 1 (HIV-1) and a subset of related simian immunodeficiency virus (SIV). The Vpu protein encoded by HIV-1 is associated with two primary functions during the viral life cycle. First, it contributes to HIV-1-induced CD4 receptor downregulation by mediating the proteasomal degradation of newly synthesized CD4 molecules in the endoplasmic reticulum (ER). Second, it enhances the release of progeny virions from infected cells by antagonizing Tetherin, an interferon (IFN)-regulated host restriction factor that directly cross-links virions on host cell-surface. This review will mostly focus on recent advances on the role of Vpu in CD4 downregulation and Tetherin antagonism and will discuss how these two functions may have impacted primate immunodeficiency virus cross-species transmission and the emergence of pandemic strain of HIV-1

Large dust particles in disks around T Tauri stars

We present 7-mm continuum observations of 14 low-mass pre-main-sequence stars in the Taurus-Auriga star-forming region obtained with the Very Large Array with ~1.5" resolution and ~0.3 mJy rms sensitivity. For 10 objects, the circumstellar emission has been spatially resolved. The large outer disk radii derived suggest that the emission at this wavelength is mostly optically thin. The millimetre spectral energy distributions are characterised by spectral indices alpha = 2.3 to 3.2. After accounting for contribution from free-free emission and corrections for optical depth, we determine dust opacity indices beta in the range 0.5 to 1.6, which suggest that millimetre-sized dust aggregates are present in the circumstellar disks. Four of the sources with beta > 1 may be consistent with submicron-sized dust as found in the interstellar medium. Our findings indicate that dust grain growth to millimetre-sized particles is completed within less than 1 Myr for the majority of circumstellar disks.Comment: 11 pages, 4 figure