Evolution and Evaluation of the Penalty Method for Alternative Graphs

Computing meaningful alternative routes in a road network is a complex problem -- already giving a clear definition of a best alternative seems to be impossible. Still, multiple methods describe how to compute reasonable alternative routes, each according to their own quality criteria. Among these methods, the penalty method has received much less attention than the via-node or plateaux based approaches. A mayor cause for the lack of interest might be the unavailability of an efficient implementation. In this paper, we take a closer look at the penalty method and extend upon its ideas. We provide the first viable implementation --suitable for interactive use-- using dynamic runtime adjustments to perform up to multiple orders of magnitude faster queries than previous implementations. Using our new implementation, we thoroughly evaluate the penalty method for its flaws and benefits

Consistent Dynamic Mode Decomposition

We propose a new method for computing Dynamic Mode Decomposition (DMD) evolution matrices, which we use to analyze dynamical systems. Unlike the majority of existing methods, our approach is based on a variational formulation consisting of data alignment penalty terms and constitutive orthogonality constraints. Our method does not make any assumptions on the structure of the data or their size, and thus it is applicable to a wide range of problems including non-linear scenarios or extremely small observation sets. In addition, our technique is robust to noise that is independent of the dynamics and it does not require input data to be sequential. Our key idea is to introduce a regularization term for the forward and backward dynamics. The obtained minimization problem is solved efficiently using the Alternating Method of Multipliers (ADMM) which requires two Sylvester equation solves per iteration. Our numerical scheme converges empirically and is similar to a provably convergent ADMM scheme. We compare our approach to various state-of-the-art methods on several benchmark dynamical systems

Telescoper: de novo assembly of highly repetitive regions.

MotivationWith advances in sequencing technology, it has become faster and cheaper to obtain short-read data from which to assemble genomes. Although there has been considerable progress in the field of genome assembly, producing high-quality de novo assemblies from short-reads remains challenging, primarily because of the complex repeat structures found in the genomes of most higher organisms. The telomeric regions of many genomes are particularly difficult to assemble, though much could be gained from the study of these regions, as their evolution has not been fully characterized and they have been linked to aging.ResultsIn this article, we tackle the problem of assembling highly repetitive regions by developing a novel algorithm that iteratively extends long paths through a series of read-overlap graphs and evaluates them based on a statistical framework. Our algorithm, Telescoper, uses short- and long-insert libraries in an integrated way throughout the assembly process. Results on real and simulated data demonstrate that our approach can effectively resolve much of the complex repeat structures found in the telomeres of yeast genomes, especially when longer long-insert libraries are used.AvailabilityTelescoper is publicly available for download at sourceforge.net/p/[email protected] informationSupplementary data are available at Bioinformatics online