309 research outputs found
Selecting universities: personal preference and rankings
Polyhedral geometry can be used to quantitatively assess the dependence of
rankings on personal preference, and provides a tool for both students and
universities to assess US News and World Report rankings
Towards the Human Genotope
The human genotope is the convex hull of all allele frequency vectors that
can be obtained from the genotypes present in the human population. In this
paper we take a few initial steps towards a description of this object, which
may be fundamental for future population based genetics studies. Here we use
data from the HapMap Project, restricted to two ENCODE regions, to study a
subpolytope of the human genotope. We study three different approaches for
obtaining informative low-dimensional projections of this subpolytope. The
projections are specified by projection onto few tag SNPs, principal component
analysis, and archetypal analysis. We describe the application of our geometric
approach to identifying structure in populations based on single nucleotide
polymorphisms
The Impact of technology on the lodging industry
This study discusses the impact of technology on the hospitality industry, with emphasis being given to the lodging industry and the effective use of hotel business centers. The study will analyze new technology and technological advances that are impacting the needs of the business traveler, the ways in which the lodging industry is addressing these needs and requirements, and trends and changes in the hospitality industry which are impacting the business traveler. This study will also attempt to answer hypotheses made concerning long term trends for business amenities in the lodging industry. Specifically the study will address the Radisson Inn, in Rochester, NY and how the Radisson can meet the needs and requirements of its business travel customers. Data has been gathered from a review of industry literature and research. Three test sites were examined, utilizing a questionnaire and site-visits, as part of a benchmarking study, and the data from these test sites has been presented. The data shows a long-term trend toward in-room amenities and away from centralized business centers. Conclusions have been made as to the data and whether it supports the hypotheses made in this study concerning business amenities at hotels. Recommendations are suggested for future studies
On the optimality of the neighbor-joining algorithm
The popular neighbor-joining (NJ) algorithm used in phylogenetics is a greedy
algorithm for finding the balanced minimum evolution (BME) tree associated to a
dissimilarity map. From this point of view, NJ is ``optimal'' when the
algorithm outputs the tree which minimizes the balanced minimum evolution
criterion. We use the fact that the NJ tree topology and the BME tree topology
are determined by polyhedral subdivisions of the spaces of dissimilarity maps
to study the optimality of the neighbor-joining
algorithm. In particular, we investigate and compare the polyhedral
subdivisions for . A key requirement is the measurement of volumes of
spherical polytopes in high dimension, which we obtain using a combination of
Monte Carlo methods and polyhedral algorithms. We show that highly unrelated
trees can be co-optimal in BME reconstruction, and that NJ regions are not
convex. We obtain the radius for neighbor-joining for and we
conjecture that the ability of the neighbor-joining algorithm to recover the
BME tree depends on the diameter of the BME tree
The Hyperdeterminant and Triangulations of the 4-Cube
The hyperdeterminant of format 2 x 2 x 2 x 2 is a polynomial of degree 24 in
16 unknowns which has 2894276 terms. We compute the Newton polytope of this
polynomial and the secondary polytope of the 4-cube. The 87959448 regular
triangulations of the 4-cube are classified into 25448 D-equivalence classes,
one for each vertex of the Newton polytope. The 4-cube has 80876 coarsest
regular subdivisions, one for each facet of the secondary polytope, but only
268 of them come from the hyperdeterminant.Comment: 30 pages, 6 figures; An author's name changed, typos fixe
Parametric Alignment of Drosophila Genomes
The classic algorithms of Needleman--Wunsch and Smith--Waterman find a
maximum a posteriori probability alignment for a pair hidden Markov model
(PHMM). In order to process large genomes that have undergone complex genome
rearrangements, almost all existing whole genome alignment methods apply fast
heuristics to divide genomes into small pieces which are suitable for
Needleman--Wunsch alignment. In these alignment methods, it is standard
practice to fix the parameters and to produce a single alignment for subsequent
analysis by biologists.
Our main result is the construction of a whole genome parametric alignment of
Drosophila melanogaster and Drosophila pseudoobscura. Parametric alignment
resolves the issue of robustness to changes in parameters by finding all
optimal alignments for all possible parameters in a PHMM. Our alignment draws
on existing heuristics for dividing whole genomes into small pieces for
alignment, and it relies on advances we have made in computing convex polytopes
that allow us to parametrically align non-coding regions using biologically
realistic models. We demonstrate the utility of our parametric alignment for
biological inference by showing that cis-regulatory elements are more conserved
between Drosophila melanogaster and Drosophila pseudoobscura than previously
thought. We also show how whole genome parametric alignment can be used to
quantitatively assess the dependence of branch length estimates on alignment
parameters.
The alignment polytopes, software, and supplementary material can be
downloaded at http://bio.math.berkeley.edu/parametric/.Comment: 19 pages, 3 figure
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