Price-and-verify: a new algorithm for recursive circle packing using Dantzig–Wolfe decomposition

This is the author accepted manuscript. The final version is available from Springer via the DOI in this record Packing rings into a minimum number of rectangles is an optimization problem which appears naturally in the logistics operations of the tube industry. It encompasses two major difficulties, namely the positioning of rings in rectangles and the recursive packing of rings into other rings. This problem is known as the Recursive Circle Packing Problem (RCPP). We present the first dedicated method for solving RCPP that provides strong dual bounds based on an exact Dantzig–Wolfe reformulation of a nonconvex mixed-integer nonlinear programming formulation. The key idea of this reformulation is to break symmetry on each recursion level by enumerating one-level packings, i.e., packings of circles into other circles, and by dynamically generating packings of circles into rectangles. We use column generation techniques to design a “price-and-verify” algorithm that solves this reformulation to global optimality. Extensive computational experiments on a large test set show that our method not only computes tight dual bounds, but often produces primal solutions better than those computed by heuristics from the literature.Federal Ministry of Education and Researc

PySCIPOpt: Mathematical Programming in Python with the SCIP Optimization Suite

This is the author accepted manuscript. The final version is available frpm Springer Verlag via the DOI in this record5th International Congress on Mathematical Software (ICMS 2016), 11-14 July 2016, Berlin, GermanySCIP is a solver for a wide variety of mathematical optimization problems. It is written in C and extendable due to its plug-in based design. However, dealing with all C specifics when extending SCIP can be detrimental to development and testing of new ideas. This paper attempts to provide a remedy by introducing PySCIPOpt, a Python interface to SCIP that enables users to write new SCIP code entirely in Python. We demonstrate how to intuitively model mixed-integer linear and quadratic optimization problems and moreover provide examples on how new Python plug-ins can be added to SCIP.German Federal Ministry of Education and Researc

A rare genomic duplication in 2p14 underlies autosomal dominant hearing loss DFNA58

Here we define a ~ 200Kb genomic duplication in 2p14 as the genetic signature that segregates with post-lingual progressive sensorineural autosomal dominant hearing loss in 20 affected individuals from the DFNA58 family, first reported in 2009. The duplication includes two entire genes, PLEK and CNRIP1, and the first exon of PPP3R1 (protein-coding), in addition to four uncharacterized long noncoding (lnc) RNA genes and part of a novel protein-coding gene. Quantitative analysis of mRNA expression in blood samples revealed selective overexpression of CNRIP1 and of two lncRNA genes (LOC107985892 and LOC102724389) in all affected members tested, but not in unaffected ones. Qualitative analysis of mRNA expression identified also fusion transcripts involving parts of PPP3R1, CNRIP1 and an intergenic region between PLEK and CNRIP1, in the blood of all carriers of the duplication, but were heterogeneous in nature. By in situ hybridization and immunofluorescence, we showed that Cnrip1, Plek and Ppp3r1 genes are all expressed in the adult mouse cochlea including the spiral ganglion neurons, suggesting changes in expression levels of these genes in the hearing organ could underlie the DFNA58 form of deafness. Our study highlights the value of studying rare genomic events leading to hearing loss such as copy number variations. Further studies will be required to determine which of these genes, either coding proteins or non-coding RNAs, is or are responsible for DFNA58 hearing loss

The ongoing pursuit of neuroprotective therapies in Parkinson disease

Many agents developed for neuroprotective treatment of Parkinson disease (PD) have shown great promise in the laboratory, but none have translated to positive results in patients with PD. Potential neuroprotective drugs, such as ubiquinone, creatine and PYM50028, have failed to show any clinical benefits in recent high-profile clinical trials. This 'failure to translate' is likely to be related primarily to our incomplete understanding of the pathogenic mechanisms underlying PD, and excessive reliance on data from toxin-based animal models to judge which agents should be selected for clinical trials. Restricted resources inevitably mean that difficult compromises must be made in terms of trial design, and reliable estimation of efficacy is further hampered by the absence of validated biomarkers of disease progression. Drug development in PD dementia has been mostly unsuccessful; however, emerging biochemical, genetic and pathological evidence suggests a link between tau and amyloid-β deposition and cognitive decline in PD, potentially opening up new possibilities for therapeutic intervention. This Review discusses the most important 'druggable' disease mechanisms in PD, as well as the most-promising drugs that are being evaluated for their potential efficiency in treatment of motor and cognitive impairments in PD

Maximizing upgrading and downgrading margins for ordinal regression

In ordinal regression, a score function and threshold values are sought to classify a set of objects into a set of ranked classes. Classifying an individual in a class with higher (respectively lower) rank than its actual rank is called an upgrading (respectively downgrading) error. Since upgrading and downgrading errors may not have the same importance, they should be considered as two different criteria to be taken into account when measuring the quality of a classifier. In Support Vector Machines, margin maximization is used as an effective and computationally tractable surrogate of the minimization of misclassification errors. As an extension, we consider in this paper the maximization of upgrading and downgrading margins as a surrogate of the minimization of upgrading and downgrading errors, and we address the biobjective problem of finding a classifier maximizing simultaneously the two margins. The whole set of Pareto-optimal solutions of such biobjective problem is described as translations of the optimal solutions of a scalar optimization problem. For the most popular case in which the Euclidean norm is considered, the scalar problem has a unique solution, yielding that all the Pareto-optimal solutions of the biobjective problem are translations of each other. Hence, the Pareto-optimal solutions can easily be provided to the analyst, who, after inspection of the misclassification errors caused, should choose in a later stage the most convenient classifier. The consequence of this analysis is that it provides a theoretical foundation for a popular strategy among practitioners, based on the so-called ROC curve, which is shown here to equal the set of Pareto-optimal solutions of maximizing simultaneously the downgrading and upgrading margins