My research interests are
at the interface of applied
and discrete probability and
problems arising in computer science
and computational biology,
with an emphasis
on discrete probability, analytic combinatorics, and asymptotic analysis. The overarching vision of my research is
a synergism of mathematics and science. My research is in nature
interdisciplinary, and has focussed on the systematic assesment of patterns in possibly non-Markovian sequences via embedding techniques, developing
computational methods associated with the prediction of RNA secondary structure,
and more recently the extrapolation
of microbial communities for meta-genomic analyses.
Keywords.
- Algorithmic and Computational Probability
- Analysis of Algorithms
- Asymptotic Analysis
- Bioinformatics
- Computational Biology
- Discrete Mathematics and Probability
- Genomics and Meta-genomics
- Mathematical Statistics
- Patterns in Non-Markovian Sequences
- RNA Secondary Structure
Active Grants.
- AMC-SS: Markovian Embeddings for the Analysis and
Computation of Patterns in non-Markovian Random Sequences. [link]
PI: M.
Lladser
- IGERT:
Interdisciplinary Quantitative Biology Program. [link]
Co-PI,
PI: T. Cech
Book
Chapters.
Mathematical
approaches for
describing microbial populations: practice and theory for extrapolation
of rich environments. [link]
M. Lladser,
R.
Knight.
In
“The Human Microbiota: How Microbial Communities Affect Health and
Disease”
Wiley-Blackwell Publishing
Edited by D. Fredricks
ISBN:
978-0-470-47989-6
ISBN-13: 978-0470479896
(2013)
Publications.
*: denotes current and former
undergraduate and graduate research assistants.
Scientific papers.
- Allocation of New Draws
for Optimal Sampling of Urn Ensembles with Application to the Human
Microbiome Project
J. Hampton*, M. E. Lladser.
Under
review (2012)
- Unifrac:
an effective distance metric for microbial
community comparison. [main
file] [supplement]
[link]
C. Lozupone, M. E. Lladser, D.
Knights, J. Stombaugh, R. Knight.
Multidisciplinary Journal of Microbial Ecology, 5:169–172
(2011)
- Chiral Histidine
selection by D-ribose RNA. [main
file] [supplement]
[link]
M. Illangasekare, R. Turk, G. C. Peterson*, M. Lladser, M. Yarus. RNA Journal,
16: 2370-2383 (2010)
- Natural and
artificial RNAs occupy the same restricted region of sequence space.
[main
file] [link]
R. Kennedy*, M. E. Lladser, Z.
Wu,
C. Zhang, M. Yarus, H. De Sterck, R.
Knight. RNA Journal, 16(2): 280–289 (2010)
- Comparison
of methods for estimating the
nucleotide substitution matrix. [main
file] [link]
M. Oscamou*, D. McDonald, V.-B. Yap, G. A. Huttley, M.
E. Lladser, R. Knight. BMC Bioinformatics, 9:511 (2008)
- Information,
probability, and the
abundance of the simplest RNA active sites. [main file] [link]
R. Kenney*, M. E. Lladser, M.
Yarus, R. Knight. Front Biosci. 13:6060-71 (2008)
Mathematics &
Applied
Mathematics papers.
- Approximation of sojourn-times via
maximal couplings: motif frequency distributions [pdf]
[link]
M. E. Lladser, S.
Chestnut*. J. Math. Biol. DOI 10.1007/s00285-013-0690-6 (2013)
- Estimation
of Distribution Overlap of Urn Models. [pdf]
[link]
J. Hampton*, M. E. Lladser.
PloS
ONE, 7(11): e42368 (2012)
- Random Cayley digraphs of diameter 2 and given degree. [pdf]
[link]
M. E. Lladser, P. Potocnik,
J.
Širáň, M. C. Wilson. Discrete Mathematics and
Theoretical Computer Science, 14:2, 83-90 (2012)
- Toward the asymptotic
count of bi-modular hidden patterns under probabilistic dynamical
sources: a case study. [pdf]
[link]
L. Lhothe, M. E. Lladser.
Discrete Mathematics and Theoretical Computer Science Proceedings, AQ:
425-452 (2012)
- Extrapolation
of urn models via Poissonization: Accurate measurements of the
microbial unknown. [pdf]
[link]
M. E. Lladser, R. Gouet, J.
Reeder. PloS ONE, 6(6): e21105 (2011)
- Occupancy
distributions in Markov chains
via Doeblin's ergodicity coefficient. [pdf]
[link]
S. Chestnut*, M. E. Lladser.
Discrete
Mathematics and Theoretical Computer Science
Proceedings, AM:79-92 (2010)
- Prediction
of unseeing proportions in urn models with
restricted sampling. [pdf]
[link]
M. E. Lladser. Proceedings
of
the 2009 Analysis of Algorithms and
Combinatorics workshop, pp. 85-91 (2009)
- Multiple
pattern matching: A
Markov chain approach. [pdf]
[link]
M. E. Lladser, M.D.
Betterton, R. Knight. J
Math Biol. 56(1-2):51-92 (2008)
- Markovian embeddings of
general random strings. [pdf]
[link]
M. E. Lladser.
Proceedings of the 2008 Analysis of Algorithms
and Combinatorics workshop, pp. 183-190 (2008)
- Semi-supervised learning
of a Markovian metric. [pdf]
[link]
A.S. Bijral*, M. E. Lladser,
G.
Grudic. 2008 SIAM
Conference on Data Mining Conference, pp. 466-471 (2008)
- Uniqueness of polynomial
cannonical representations. [pdf]
[link]
M. E. Lladser. 2007
Conference
on Analysis of Algorithms, Discrete
Mathematics and Theoretical Computer Science
Proceedings, AH, 463-470 (2007)
- Minimal Markov chain
embeddings of pattern problems [pdf]
[link]
M. E. Lladser. Proceedings
of
the 2007 Information Theory and Applications
Workshop, University of California, San Diego (2007)
- Mixed powers of
generating functions. [pdf]
[link]
M. E. Lladser. Discrete
Mathematics and Theoretical Computer Science
Proceedings, AG, 171-182 (2006)
- Uniform
formulae for
coefficients of meromorphic functions in two variables. Part I. [pdf]
[link]
M. E. Lladser. SIAM J.
Discrete Math. 20, 811-828 (2006)
- Domain of
attraction of the
quasi-stationary distributions of the Ornstein-Uhlenbeck process. [pdf]
[link]
M. E. Lladser and J. San
Martin. Journal of Applied Probability,
Vol. 37, No. 2, 511-520 (2000)
Theses.
- Asymptotic
enumeration via
singularity analysis. [pdf]
M. E. Lladser. Ph.D.
dissertation, The Ohio State University
(2003)
Graduate Advisor: Dr. Robin Pemantle
- Dominio de
atracción de las distribuciones quasi-estacionarias del processo
del Ornstein-Uhlenbeck.
M. E. Lladser.
Thesis
for the professional degree of
Mathematical Civil Engineering, Universidad de Chile (1996)
Undergraduate Advisor: Dr. Jaime San Martin
Former
students theses.
- Dissimilarity and
optimal sampling in urn models. [pdf] [link]
Jerrad Hampton, Ph.D. in Applied Mathematics, University of Colorado
(2012)
- Approximating Markov
chain occupancy distributions. [link]
Stephen Chestnut, M.S. in Applied Mathematics, University of Colorado
(2010)
- Fairness Analysis via
Poissonization. [link]
Geoffrey C.L. Peterson, M.S. in Applied Mathematics,
University of Colorado (2010)
- Calculating RNA motif probabilities and recognizing
patterns in sequence data. [pdf]
R. Kennedy, B.S. in Computer Science, University of Colorado (2009)
Books.
Variables Aletorias y
Simulación Estocástica (translation: Random Variables and Stochastic Simulation)
[link]
Author: M. E. Lladser
Editor: Noreste Juan Carlos Sáez, Chile
Edition: First.
Pages: 207
Language: Spanish
ISBN: 9789563060683
E-book
download
Order
hardcopy (Chile)
Edited Volumes.
Algorithmic
Probability and Combinatorics. [link]
AMS Contemporary Mathematics, Volume 520, 240 pp. (2010)
Editors: M. E. Lladser,
R. Maier, M.
Mishna, A. Rechnitzer.
Recent
Conferences/Seminars/Workshops.
- Mathematics and Statistics Colloquium, Bowling Green State
University, NOV/2012
- 2012 RNA Workshop, Benasque, Spain,
JUL-AUG/2012
- 8th International Purdue Symposium on Statistics, Purdue,
JUN/2012
- 23rd International Meeting on Probabilistic, Combinatorial
and Asymptotic Methods for the Analysis of Algorithms, University of
Montreal, Canada, JUN/2012
- 2012 International Workshop on Applied Probability,
Jerusalem, Israel, JUN/2012
- 22th International Meeting on Probabilistic,
Combinatorial, and Asymptotic Methods in the Analysis of Algorithms,
Bedlewo, Poland, JUN/2011
- 22nd International Meeting on Probabilistic,
Combinatorial, and Asymptotic Methods in the Analysis of Algorithms,
Bedlewo, Poland, JUN/2011 (speaker: J. Hampton)
- 15th International Conference on Random
Structures and Algorithms, Emory University, Atlanta, JUN/2011
- Seminar of Stochastic Modeling, Center of
Mathematical Modeling, Chile, JUN/2011
- 2011 Frontier Probability Days, Salt Lake
City, Utah, MAR/2011
- Mathematics Colloquium, Iowa State University,
MAR/2011
- Statistics Seminar, Colorado State University,
Fort Collins, FEB/2011
- Science Short Presentation, CIMB meeting,
DEC/2010
- CIMBposium Poster Session, University of
Colorado - Boulder, NOV/2010 (speaker: J.
Hampton)
- Bioinformatics Supergroup, University of
Colorado - Boulder, OCT/2010
- Combinatorics and Probability Seminar,
Department of Mathematics, University of Pennsylvania, SEP/2010
- 21st International Meeting on Probabilistic,
Combinatorial, and Asymptotic Methods in the Analysis of Algorithms,
Vienna, Austria, JUN/2010
- Séminaire d'algorithmique,
Département d'informatique, University of Caen, France, JUN/2010
- Probability and Statistics Seminar, Department
of Mathematics, University of Colorado - Boulder, APR/2010
- SIAM's Graduate Chapter, University of
Colorado - Boulder, MAR/2010 (speaker: S. Chestnut)
- Combinatorics Seminar, Laboratoire Bordelais de Recherche
en Informatique, Université Bordeaux 1, Bordeaux, France,
FEB/2010
- Butcher Symposium on Genomics and Biotechnology,
University of Colorado, NOV/2009
- Bioinformatics Supergroup, University of Colorado,
NOV/2009 (speaker: G. C. Peterson)
- 20th International Conference on Probabilistic,
Combinatorial,
and Asymptotic Methods in the Analysis of Algorithms, Fréjus,
France,
JUN/2009
- Fields-MITACS Summer School in Applied Probability,
Department of Mathematics, University of Carleton, Canada, MAY/09
(speaker: A. Sen)
- Fields-MITACS Summer School in Applied Probability,
Department
of Mathematics, University of Carleton, Canada, MAY/09 (speaker: J.
Hampton)
- Fields-MITACS Summer School in Applied Probability,
Department
of Mathematics, University of Carleton, Canada, MAY/09 (speaker: S.
Chestnut)
- Applied Mathematics Colloquium, University of Colorado,
APR/2009
- Department of Informatics, University of Caen, France,
MAR/2009
- 2009 Analysis of Algorithms and Combinatorics Workshop,
New York, JAN/2009
Looking
for thesis advisor? ...
If you are an APPM PhD or Master student, or an IQ Biology student and
have some interests in
any of the keywords above, please feel free to
contact me.
Advisory for students in other departments or programs is also very
welcome and
only subject to common ground interests and time availability.
"I was as
working
on the proof of one of my poems all the morning, and
took out a comma. In the
afternoon I put it back
again."
-
CONVERSATION
