Node-weighted Steiner tree and group Steiner tree in planar graphs

We improve the approximation ratios for two optimization problems in planar graphs. For node-weighted Steiner tree, a classical network-optimization problem, the best achievable approximation ratio in general graphs is Θ [theta] (logn), and nothing better was previously known for planar graphs. We give a constant-factor approximation for planar graphs. Our algorithm generalizes to allow as input any nontrivial minor-closed graph family, and also generalizes to address other optimization problems such as Steiner forest, prize-collecting Steiner tree, and network-formation games. The second problem we address is group Steiner tree: given a graph with edge weights and a collection of groups (subsets of nodes), find a minimum-weight connected subgraph that includes at least one node from each group. The best approximation ratio known in general graphs is O(log3 [superscript 3] n), or O(log2 [superscript 2] n) when the host graph is a tree. We obtain an O(log n polyloglog n) approximation algorithm for the special case where the graph is planar embedded and each group is the set of nodes on a face. We obtain the same approximation ratio for the minimum-weight tour that must visit each group

Magmatic evolution of the Nevado del Ruiz volcano, Central Cordillera, Colombia : mineral chemistry and geochemistry

A partir de nouvelles données pétrographiques, minéralogiques et géochimiques, les auteurs réalisent une caractérisation géochimique des laves du Nevado del Ruiz (éruptions quaternaires, historiques et récentes) et des formations volcaniques du Pliocène des pentes de la Cordillère central

Translational and Regulatory Challenges for Exon Skipping Therapies

Several translational challenges are currently impeding the therapeutic development of antisense-mediated exon skipping approaches for rare diseases. Some of these are inherent to developing therapies for rare diseases, such as small patient numbers and limited information on natural history and interpretation of appropriate clinical outcome measures. Others are inherent to the antisense oligonucleotide (AON)-mediated exon skipping approach, which employs small modified DNA or RNA molecules to manipulate the splicing process. This is a new approach and only limited information is available on long-term safety and toxicity for most AON chemistries. Furthermore, AONs often act in a mutation-specific manner, in which case multiple AONs have to be developed for a single disease. A workshop focusing on preclinical development, trial design, outcome measures, and different forms of marketing authorization was organized by the regulatory models and biochemical outcome measures working groups of Cooperation of Science and Technology Action: "Networking towards clinical application of antisense-mediated exon skipping for rare diseases." The workshop included participants from patient organizations, academia, and members of staff from the European Medicine Agency and Medicine Evaluation Board (the Netherlands). This statement article contains the key outcomes of this meeting.status: publishe

Spotting Trees with Few Leaves

We show two results related to the Hamiltonicity and $k$-Path algorithms in undirected graphs by Bj\"orklund [FOCS'10], and Bj\"orklund et al., [arXiv'10]. First, we demonstrate that the technique used can be generalized to finding some $k$-vertex tree with $l$ leaves in an $n$-vertex undirected graph in $O^*(1.657^k2^{l/2})$ time. It can be applied as a subroutine to solve the $k$-Internal Spanning Tree ($k$-IST) problem in $O^*(\min(3.455^k, 1.946^n))$ time using polynomial space, improving upon previous algorithms for this problem. In particular, for the first time we break the natural barrier of $O^*(2^n)$. Second, we show that the iterated random bipartition employed by the algorithm can be improved whenever the host graph admits a vertex coloring with few colors; it can be an ordinary proper vertex coloring, a fractional vertex coloring, or a vector coloring. In effect, we show improved bounds for $k$-Path and Hamiltonicity in any graph of maximum degree $\Delta=4,\ldots,12$ or with vector chromatic number at most 8

Fast Distributed Approximation for Max-Cut

Finding a maximum cut is a fundamental task in many computational settings. Surprisingly, it has been insufficiently studied in the classic distributed settings, where vertices communicate by synchronously sending messages to their neighbors according to the underlying graph, known as the $\mathcal{LOCAL}$ or $\mathcal{CONGEST}$ models. We amend this by obtaining almost optimal algorithms for Max-Cut on a wide class of graphs in these models. In particular, for any $\epsilon > 0$, we develop randomized approximation algorithms achieving a ratio of $(1-\epsilon)$ to the optimum for Max-Cut on bipartite graphs in the $\mathcal{CONGEST}$ model, and on general graphs in the $\mathcal{LOCAL}$ model. We further present efficient deterministic algorithms, including a $1/3$-approximation for Max-Dicut in our models, thus improving the best known (randomized) ratio of $1/4$. Our algorithms make non-trivial use of the greedy approach of Buchbinder et al. (SIAM Journal on Computing, 2015) for maximizing an unconstrained (non-monotone) submodular function, which may be of independent interest

Stochastic Budget Optimization in Internet Advertising

Internet advertising is a sophisticated game in which the many advertisers "play" to optimize their return on investment. There are many "targets" for the advertisements, and each "target" has a collection of games with a potentially different set of players involved. In this paper, we study the problem of how advertisers allocate their budget across these "targets". In particular, we focus on formulating their best response strategy as an optimization problem. Advertisers have a set of keywords ("targets") and some stochastic information about the future, namely a probability distribution over scenarios of cost vs click combinations. This summarizes the potential states of the world assuming that the strategies of other players are fixed. Then, the best response can be abstracted as stochastic budget optimization problems to figure out how to spread a given budget across these keywords to maximize the expected number of clicks. We present the first known non-trivial poly-logarithmic approximation for these problems as well as the first known hardness results of getting better than logarithmic approximation ratios in the various parameters involved. We also identify several special cases of these problems of practical interest, such as with fixed number of scenarios or with polynomial-sized parameters related to cost, which are solvable either in polynomial time or with improved approximation ratios. Stochastic budget optimization with scenarios has sophisticated technical structure. Our approximation and hardness results come from relating these problems to a special type of (0/1, bipartite) quadratic programs inherent in them. Our research answers some open problems raised by the authors in (Stochastic Models for Budget Optimization in Search-Based Advertising, Algorithmica, 58 (4), 1022-1044, 2010).Comment: FINAL versio

Longitudinal effect of eteplirsen versus historical control on ambulation in Duchenne muscular dystrophy

To continue evaluation of the long-term efficacy and safety of eteplirsen, a phosphorodiamidate morpholino oligomer designed to skip DMD exon 51 in patients with Duchenne muscular dystrophy (DMD). Three-year progression of eteplirsen-treated patients was compared to matched historical controls (HC). METHODS: Ambulatory DMD patients who were 657 years old and amenable to exon 51 skipping were randomized to eteplirsen (30/50mg/kg) or placebo for 24 weeks. Thereafter, all received eteplirsen on an open-label basis. The primary functional assessment in this study was the 6-Minute Walk Test (6MWT). Respiratory muscle function was assessed by pulmonary function testing (PFT). Longitudinal natural history data were used for comparative analysis of 6MWT performance at baseline and months 12, 24, and 36. Patients were matched to the eteplirsen group based on age, corticosteroid use, and genotype. RESULTS: At 36 months, eteplirsen-treated patients (n = 12) demonstrated a statistically significant advantage of 151m (p < 0.01) on 6MWT and experienced a lower incidence of loss of ambulation in comparison to matched HC (n = 13) amenable to exon 51 skipping. PFT results remained relatively stable in eteplirsen-treated patients. Eteplirsen was well tolerated. Analysis of HC confirmed the previously observed change in disease trajectory at age 7 years, and more severe progression was observed in patients with mutations amenable to exon skipping than in those not amenable. The subset of patients amenable to exon 51 skipping showed a more severe disease course than those amenable to any exon skipping. INTERPRETATION: Over 3 years of follow-up, eteplirsen-treated patients showed a slower rate of decline in ambulation assessed by 6MWT compared to untreated matched HC. Ann Neurol 2016;79:257-271

Duchenne muscular dystrophy

Duchenne muscular dystrophy is a severe, progressive, muscle-wasting disease that leads to difficulties with movement and, eventually, to the need for assisted ventilation and premature death. The disease is caused by mutations in DMD (encoding dystrophin) that abolish the production of dystrophin in muscle. Muscles without dystrophin are more sensitive to damage, resulting in progressive loss of muscle tissue and function, in addition to cardiomyopathy. Recent studies have greatly deepened our understanding of the primary and secondary pathogenetic mechanisms. Guidelines for the multidisciplinary care for Duchenne muscular dystrophy that address obtaining a genetic diagnosis and managing the various aspects of the disease have been established. In addition, a number of therapies that aim to restore the missing dystrophin protein or address secondary pathology have received regulatory approval and many others are in clinical development.Duchenne muscular dystrophy is an X-linked progressive, muscle-wasting disease that manifests in childhood as difficulties with movement. This Primer by Aartsma-Rus and colleagues discusses the clinical presentation, epidemiology, pathophysiology, genetic diagnosis and treatment of this disorder.Functional Genomics of Muscle, Nerve and Brain Disorder

Projection methods in conic optimization

There exist efficient algorithms to project a point onto the intersection of a convex cone and an affine subspace. Those conic projections are in turn the work-horse of a range of algorithms in conic optimization, having a variety of applications in science, finance and engineering. This chapter reviews some of these algorithms, emphasizing the so-called regularization algorithms for linear conic optimization, and applications in polynomial optimization. This is a presentation of the material of several recent research articles; we aim here at clarifying the ideas, presenting them in a general framework, and pointing out important techniques