A hybrid constraint programming and semidefinite programming approach for the stable set problem

This work presents a hybrid approach to solve the maximum stable set problem, using constraint and semidefinite programming. The approach consists of two steps: subproblem generation and subproblem solution. First we rank the variable domain values, based on the solution of a semidefinite relaxation. Using this ranking, we generate the most promising subproblems first, by exploring a search tree using a limited discrepancy strategy. Then the subproblems are being solved using a constraint programming solver. To strengthen the semidefinite relaxation, we propose to infer additional constraints from the discrepancy structure. Computational results show that the semidefinite relaxation is very informative, since solutions of good quality are found in the first subproblems, or optimality is proven immediately.Comment: 14 page

Management of cerebral azole-resistant Aspergillus fumigatus infection : a role for intraventricular liposomal-amphotericin B

Objectives: In the pre-azole era, central nervous system (CNS) infections with Aspergillus had a dismal outcome. Survival improved with voriconazole but CNS infections caused by azole-resistant Aspergillus fumigatus preclude its use. Intravenous liposomal-amphotericin B (L-AmB) is the preferred treatment option for azole-resistant CNS infections but has suboptimal brain concentrations. Methods: We describe three patients with biopsy-proven CNS aspergillosis where intraventricular L-AmB was added to systemic therapy. Two patients with azole-resistant aspergillosis and one patient with azole-susceptible CNS aspergillosis were treated with intraventricular L-AmB at a dose of 1 mg weekly. Results: We describe three patients successfully treated with a combination of intravenous and intraventricular L-AmB. All three patients survived but one patient developed serious headaches, most likely not related to this treatment. Conclusions: Intraventricular L-AmB may have a role in the treatment of therapy-refractory CNS aspergillosis when added to systemic therapy. (C) 2020 The Author(s). Published by Elsevier Ltd on behalf of International Society for Antimicrobial Chemotherapy

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

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

Combination antisense treatment for destructive exon skipping of myostatin and open reading frame rescue of dystrophin in neonatal <i>mdx</i> mice

The fatal X-linked Duchenne muscular dystrophy (DMD), characterized by progressive muscle wasting and muscle weakness, is caused by mutations within the DMD gene. The use of antisense oligonucleotides (AOs) modulating pre-mRNA splicing to restore the disrupted dystrophin reading frame, subsequently generating a shortened but functional protein has emerged as a potential strategy in DMD treatment. AO therapy has recently been applied to induce out-of-frame exon skipping of myostatin pre-mRNA, knocking-down expression of myostatin protein, and such an approach is suggested to enhance muscle hypertrophy/hyperplasia and to reduce muscle necrosis. Within this study, we investigated dual exon skipping of dystrophin and myostatin pre-mRNAs using phosphorodiamidate morpholino oligomers conjugated with an arginine-rich peptide (B-PMOs). Intraperitoneal administration of B-PMOs was performed in neonatal mdx males on the day of birth, and at weeks 3 and 6. At week 9, we observed in treated mice (as compared to age-matched, saline-injected controls) normalization of muscle mass, a recovery in dystrophin expression, and a decrease in muscle necrosis, particularly in the diaphragm. Our data provide a proof of concept for antisense therapy combining dystrophin restoration and myostatin inhibition for the treatment of DMD

Ataluren delays loss of ambulation and respiratory decline in nonsense mutation Duchenne muscular dystrophy patients

Aim: We investigated the effect of ataluren plus standard of care (SoC) on age at loss of ambulation (LoA) and respiratory decline in patients with nonsense mutation Duchenne muscular dystrophy (nmDMD) versus patients with DMD on SoC alone. / Patients & methods: Study 019 was a long-term Phase III study of ataluren safety in nmDMD patients with a history of ataluren exposure. Propensity score matching identified Study 019 and CINRG DNHS patients similar in disease progression predictors. / Results & conclusion: Ataluren plus SoC was associated with a 2.2-year delay in age at LoA (p = 0.0006), and a 3.0-year delay in decline of predicted forced vital capacity to <60% in nonambulatory patients (p = 0.0004), versus SoC. Ataluren plus SoC delays disease progression and benefits ambulatory and nonambulatory patients with nmDMD. / ClinicalTrials.gov: NCT01557400

Nonlinear Integer Programming

Research efforts of the past fifty years have led to a development of linear integer programming as a mature discipline of mathematical optimization. Such a level of maturity has not been reached when one considers nonlinear systems subject to integrality requirements for the variables. This chapter is dedicated to this topic. The primary goal is a study of a simple version of general nonlinear integer problems, where all constraints are still linear. Our focus is on the computational complexity of the problem, which varies significantly with the type of nonlinear objective function in combination with the underlying combinatorial structure. Numerous boundary cases of complexity emerge, which sometimes surprisingly lead even to polynomial time algorithms. We also cover recent successful approaches for more general classes of problems. Though no positive theoretical efficiency results are available, nor are they likely to ever be available, these seem to be the currently most successful and interesting approaches for solving practical problems. It is our belief that the study of algorithms motivated by theoretical considerations and those motivated by our desire to solve practical instances should and do inform one another. So it is with this viewpoint that we present the subject, and it is in this direction that we hope to spark further research.Comment: 57 pages. To appear in: M. J\"unger, T. Liebling, D. Naddef, G. Nemhauser, W. Pulleyblank, G. Reinelt, G. Rinaldi, and L. Wolsey (eds.), 50 Years of Integer Programming 1958--2008: The Early Years and State-of-the-Art Surveys, Springer-Verlag, 2009, ISBN 354068274

A Fresh Variational-Analysis Look at the Positive Semidefinite Matrices World

International audienceEngineering sciences and applications of mathematics show unambiguously that positive semidefiniteness of matrices is the most important generalization of non-negative real num- bers. This notion of non-negativity for matrices has been well-studied in the literature; it has been the subject of review papers and entire chapters of books. This paper reviews some of the nice, useful properties of positive (semi)definite matrices, and insists in particular on (i) characterizations of positive (semi)definiteness and (ii) the geometrical properties of the set of positive semidefinite matrices. Some properties that turn out to be less well-known have here a special treatment. The use of these properties in optimization, as well as various references to applications, are spread all the way through. The "raison d'être" of this paper is essentially pedagogical; it adopts the viewpoint of variational analysis, shedding new light on the topic. Important, fruitful, and subtle, the positive semidefinite world is a good place to start with this domain of applied mathematics

A molecular phylogeny of the cicadas (Hemiptera: Cicadidae) with a review of tribe and subfamily classification:

A molecular phylogeny and a review of family-group classification are presented for 137 species (ca. 125 genera) of the insect family Cicadidae, the true cicadas, plus two species of hairy cicadas (Tettigarctidae) and two outgroup species from Cercopidae. Five genes, two of them mitochondrial, comprise the 4992 base-pair molecular dataset. Maximum-likelihood and Bayesian phylogenetic results are shown, including analyses to address potential base composition bias. Tettigarcta is confirmed as the sister-clade of the Cicadidae and support is found for three subfamilies identified in an earlier morphological cladistic analysis. A set of paraphyletic deep-level clades formed by African genera are together named as Tettigomyiinae n. stat. Taxonomic reassignments of genera and tribes are made where morphological examination confirms incorrect placements suggested by the molecular tree, and 11 new tribes are defined (Arenopsaltriini n. tribe, Durangonini n. tribe, Katoini n. tribe, Lacetasini n. tribe, Macrotristriini n. tribe, Malagasiini n. tribe, Nelcyndanini n. tribe, Pagiphorini n. tribe, Pictilini n. tribe, Psaltodini n. tribe, and Selymbriini n. tribe). Tribe Tacuini n. syn. is synonymized with Cryptotympanini, and Tryellina n. syn. is synonymized with an expanded Tribe Lamotialnini. Tribe Hyantiini n. syn. is synonymized with Fidicinini. Tribe Sinosenini is transferred to Cicadinae from Cicadettinae, Cicadatrini is moved to Cicadettinae from Cicadinae, and Ydiellini and Tettigomyiini are transferred to Tettigomyiinae n. stat from Cicadettinae. While the subfamily Cicadinae, historically defined by the presence of timbal covers, is weakly supported in the molecular tree, high taxonomic rank is not supported for several earlier clades based on unique morphology associated with sound production

Meta-analyses of ataluren randomized controlled trials in nonsense mutation Duchenne muscular dystrophy.

Aim: Assess the totality of efficacy evidence for ataluren in patients with nonsense mutation Duchenne muscular dystrophy (nmDMD). Materials & methods: Data from the two completed randomized controlled trials (ClinicalTrials.gov: NCT00592553; NCT01826487) of ataluren in nmDMD were combined to examine the intent-to-treat (ITT) populations and two patient subgroups (baseline 6-min walk distance [6MWD] \u3e= 300-\u3c400 or \u3c400 m). Meta-analyses examined 6MWD change from baseline to week 48.Results:Statistically significant differences in 6MWD change with ataluren versus placebo were observed across all three meta-analyses. Least-squares mean difference (95% CI): ITT (n = 342), +17.2 (0.2-34.1) m, p = 0.0473; \u3e= 300-\u3c400 m (n = 143), +43.9 (18.2-69.6) m, p = 0.0008; \u3c400 m (n = 216), +27.7 (6.4-49.0) m, p = 0.0109. Conclusion: These meta-analyses support previous evidence for ataluren in slowing disease progression versus placebo in patients with nmDMD over 48 weeks. Treatment benefit was most evident in patients with a baseline 6MWD \u3e= 300-\u3c400 m (the ambulatory transition phase), thereby informing future trial design