Graph algorithms for DNA sequencing – origins,current models and the future

With the ubiquitous presence of next-generation sequencing in modern biological, genetic, pharmaceutical and medical research, not everyone pays attention to the underlying computational methods. Even fewer researchers know what were the origins of the current models for DNA assembly. We present original graph models used in DNA sequencing by hybridization, discuss their properties and connections between them. We also explain how these graph models evolved to adapt to the characteristics of next-generation sequencing. Moreover, we present a practical comparison of state-of-the-art DNA de novo assembly tools representing these transformed models, i.e. overlap and decomposition-based graphs. Even though the competition is tough, some assemblers perform better and certainly large differences may be observed in hardware resources utilization. Finally, we outline the most important trends in the sequencing field, and try to predict their impact on the computational models in the future.     

Learning beginning algebra in a computer-intensive environment

We present a design research on learning beginning algebra in an environment where spreadsheets were available at all times but the decision about using them or not, and how, in any particular situation was left to the students. Students’ activity is analyzed in Kieran’s framework of generational, transformational and global/meta-level activity, and compared to the designers’ intentions. We do this by focusing on the activity of one student in four sessions spread over several months and discussing the activity of 51 additional students in view of the analysis of the focus student. We show that the environment enables a number of different entries into algebra and as such supports students in becoming autonomous learners of algebra, and in making the shift from arithmetic to algebra via generational and global/meta-level activity before dealing with the more technical transformational activities.     

Finite element analysis of varitional crimes for a quasilinear elliptic problem in 3D

Summary. We examine a finite element approximation of a quasilinear boundary value elliptic problem in a three-dimensional bounded convex domain with a smooth boundary. The domain is approximated by a polyhedron and a numerical integration is taken into account. We apply linear tetrahedral finite elements and prove the convergence of approximate solutions on polyhedral domains in the -norm to the true solution without any additional regularity assumptions. Received May 23, 1997 / Published online December 6, 1999     

On uniformly Gâteaux smooth norms and normal structure

It is shown that every separable Banach space admits an equivalent norm that is uniformly Gâteaux smooth and yet lacks asymptotic normal structure.

     

Coulomb analogy for non-Hermitian degeneracies near quantum phase transitions

Degeneracies near the real axis in a complex-extended parameter space of a Hermitian Hamiltonian are studied. We present a method to measure distributions of such degeneracies on the Riemann sheet of a selected level and apply it in classification of quantum phase transitions. The degeneracies are shown to behave similarly as complex zeros of a partition function.