Faculty Research Publications (Mathematics)
http://hdl.handle.net/1957/13818
2015-04-27T00:04:51ZDispersion reducing methods for edge discretizations of the electric vector wave equation
http://hdl.handle.net/1957/55664
Dispersion reducing methods for edge discretizations of the electric vector wave equation
Bokil, V. A.; Gibson, N. L.; Gyrya, V.; McGregor, D. A.
We present a novel strategy for minimizing the numerical dispersion error in edge
discretizations of the time-domain electric vector wave equation on square meshes
based on the mimetic finite difference (MFD) method. We compare this strategy, called
M-adaptation, to two other discretizations, also based on square meshes. One is the lowest
order Nédélec edge element discretization. The other is a modified quadrature approach
(GY-adaptation) proposed by Guddati and Yue for the acoustic wave equation in two
dimensions. All three discrete methods use the same edge-based degrees of freedom, while
the temporal discretization is performed using the standard explicit Leapfrog scheme. To
obtain efficient and explicit time stepping methods, the three schemes are further mass
lumped. We perform a dispersion and stability analysis for the presented schemes and
compare all three methods in terms of their stability regions and phase error. Our results
indicate that the method produced by GY-adaptation and the Nédélec method are both
second order accurate for numerical dispersion, but differ in the order of their numerical
anisotropy (fourth order, versus second order, respectively). The result of M-adaptation is
a discretization that is fourth order accurate for numerical dispersion as well as numerical
anisotropy. Numerical simulations are provided that illustrate the theoretical results.
To the best of our knowledge, one or more authors of this paper were federal employees when contributing to this work. This is the publisher’s final pdf. The published article is copyrighted by Elsevier and can be found at: http://www.journals.elsevier.com/journal-of-computational-physics.
2015-04-15T00:00:00ZInequalities for positive rank and crank moments of overpartitions
http://hdl.handle.net/1957/55598
Inequalities for positive rank and crank moments of overpartitions
Larsen, Acadia; Rust, Alexa; Swisher, Holly
In recent work, Andrews, Chan, and Kim extend a result of Garvan about even rank
and crank moments of partitions to positive moments. In a similar fashion we extend a
result of Mao about even rank moments of overpartitions. We investigate positive Dyson-rank,
M₂-rank, first residual crank, and second residual crank moments of overpartitions.
In particular, we prove a conjecture of Mao which states that the positive Dyson-rank
moments are larger than the positive M₂-rank moments. We also prove some additional
inequalities involving rank and crank moments of overpartitions, including an interlacing
property.
This is an author's peer-reviewed final manuscript, as accepted by the publisher. The published article is copyrighted by the World Scientific Publishing Company and can be found at: http://www.worldscientific.com/worldscinet/ijnt
2014-12-01T00:00:00ZSEK: sparsity exploiting k-mer-based estimation of bacterial community composition
http://hdl.handle.net/1957/55141
SEK: sparsity exploiting k-mer-based estimation of bacterial community composition
Chatterjee, Saikat; Koslicki, David; Dong, Siyuan; et al.
MOTIVATION: Estimation of bacterial community composition from
a high-throughput sequenced sample is an important task in
metagenomics applications. Since the sample sequence data
typically harbors reads of variable lengths and different levels of
biological and technical noise, accurate statistical analysis of such
data is challenging. Currently popular estimation methods are
typically very time consuming in a desktop computing environment.
RESULTS: Using sparsity enforcing methods from the general sparse
signal processing field (such as compressed sensing), we derive
a solution to the community composition estimation problem by a
simultaneous assignment of all sample reads to a pre-processed
reference database. A general statistical model based on kernel
density estimation techniques is introduced for the assignment task
and the model solution is obtained using convex optimization tools.
Further, we design a greedy algorithm solution for a fast solution. Our
approach offers a reasonably fast community composition estimation
method which is shown to be more robust to input data variation than
a recently introduced related method.
AVAILABILITY: A platform-independent Matlab implementation of the
method is freely available at http://www.ee.kth.se/ctsoftware; source
code that does not require access to Matlab is currently being tested
and will be made available later through the above website.
This is a pre-copy-editing, author-produced PDF of an article accepted for publication in Bioinformatics following peer review. The definitive publisher-authenticated version, Chatterjee, S., Koslicki, D., Dong, S., Innocenti, N., Cheng, L., Lan, Y., ... & Corander, J. (2014). SEK: Sparsity exploiting k-mer-based estimation of bacterial community composition. Bioinformatics, 30(17), 2423-2431. doi:10.1093/bioinformatics/btu320, is available online at: http://bioinformatics.oxfordjournals.org/content/30/17/2423.
The published article is copyrighted by the Author(s) and published by Oxford University Press.
2014-09-01T00:00:00ZCoding sequence density estimation via topological pressure
http://hdl.handle.net/1957/55140
Coding sequence density estimation via topological pressure
Koslicki, David; Thompson, Daniel J.
We give a new approach to coding sequence (CDS) density
estimation in genomic analysis based on the topological pressure, which
we develop from a well known concept in ergodic theory. Topological
pressure measures the ‘weighted information content’ of a finite word,
and incorporates 64 parameters which can be interpreted as a choice
of weight for each nucleotide triplet. We train the parameters so that
the topological pressure fits the observed coding sequence density on
the human genome, and use this to give ab initio predictions of CDS
density over windows of size around 66,000bp on the genomes of Mus
Musculus, Rhesus Macaque and Drososphilia Melanogaster. While the
differences between these genomes are too great to expect that training
on the human genome could predict, for example, the exact locations of
genes, we demonstrate that our method gives reasonable estimates for
the ‘coarse scale’ problem of predicting CDS density.
Inspired again by ergodic theory, the weightings of the nucleotide
triplets obtained from our training procedure are used to define a probability
distribution on finite sequences, which can be used to distinguish
between intron and exon sequences from the human genome of lengths
between 750bp and 5,000bp. At the end of the paper, we explain the
theoretical underpinning for our approach, which is the theory of Thermodynamic
Formalism from the dynamical systems literature. Mathematica
and MATLAB implementations of our method are available at
http://sourceforge.net/projects/topologicalpres/.
This is an author's peer-reviewed final manuscript, as accepted by the publisher. The published article is copyrighted by Springer and can be found at: http://link.springer.com/journal/285
2015-01-01T00:00:00Z