4,317 research outputs found
Partial DNA Assembly: A Rate-Distortion Perspective
Earlier formulations of the DNA assembly problem were all in the context of
perfect assembly; i.e., given a set of reads from a long genome sequence, is it
possible to perfectly reconstruct the original sequence? In practice, however,
it is very often the case that the read data is not sufficiently rich to permit
unambiguous reconstruction of the original sequence. While a natural
generalization of the perfect assembly formulation to these cases would be to
consider a rate-distortion framework, partial assemblies are usually
represented in terms of an assembly graph, making the definition of a
distortion measure challenging. In this work, we introduce a distortion
function for assembly graphs that can be understood as the logarithm of the
number of Eulerian cycles in the assembly graph, each of which correspond to a
candidate assembly that could have generated the observed reads. We also
introduce an algorithm for the construction of an assembly graph and analyze
its performance on real genomes.Comment: To be published at ISIT-2016. 11 pages, 10 figure
Structure-Preserving Discretization of Incompressible Fluids
The geometric nature of Euler fluids has been clearly identified and
extensively studied over the years, culminating with Lagrangian and Hamiltonian
descriptions of fluid dynamics where the configuration space is defined as the
volume-preserving diffeomorphisms, and Kelvin's circulation theorem is viewed
as a consequence of Noether's theorem associated with the particle relabeling
symmetry of fluid mechanics. However computational approaches to fluid
mechanics have been largely derived from a numerical-analytic point of view,
and are rarely designed with structure preservation in mind, and often suffer
from spurious numerical artifacts such as energy and circulation drift. In
contrast, this paper geometrically derives discrete equations of motion for
fluid dynamics from first principles in a purely Eulerian form. Our approach
approximates the group of volume-preserving diffeomorphisms using a finite
dimensional Lie group, and associated discrete Euler equations are derived from
a variational principle with non-holonomic constraints. The resulting discrete
equations of motion yield a structure-preserving time integrator with good
long-term energy behavior and for which an exact discrete Kelvin's circulation
theorem holds
FEA modeling of orthogonal cutting of steel: a review
Orthogonal cutting is probably the most studied machining operation for metals. Its simulation with the Finite Element Analysis (FEA) method is of paramount academic interest. 2D models, and to a lesser extent 3D models, have been developed to predict cutting forces, chip formation, heat generation and temperature fields, residual stress distribution and tool wear. This paper first presents a brief review of scientific literature with focus on FEA modelling of the orthogonal cutting process for steels. Following, emphasis is put on the building blocks of the simulation model, such as the formulation of the mechanical problem, the material constitutive model, the friction models and damage laws
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