195 research outputs found
Optimal distance query reconstruction for graphs without long induced cycles
Let be an -vertex connected graph of maximum degree .
Given access to and an oracle that given two vertices , returns
the shortest path distance between and , how many queries are needed to
reconstruct ? We give a simple deterministic algorithm to reconstruct trees
using distance queries and show that even
randomised algorithms need to use at least
queries in expectation. The best previous lower bound was an
information-theoretic lower bound of . Our lower
bound also extends to related query models including distance queries for
phylogenetic trees, membership queries for learning partitions and path queries
in directed trees.
We extend our deterministic algorithm to reconstruct graphs without induced
cycles of length at least using queries, which
includes various graph classes of interest such as chordal graphs, permutation
graphs and AT-free graphs. Since the previously best known randomised algorithm
for chordal graphs uses queries in expectation, we both
get rid off the randomness and get the optimal dependency in for chordal
graphs and various other graph classes.
Finally, we build on an algorithm of Kannan, Mathieu, and Zhou [ICALP, 2015]
to give a randomised algorithm for reconstructing graphs of treelength
using queries in expectation.Comment: 35 page
Exact antichain saturation numbers via a generalisation of a result of Lehman-Ron
For given positive integers and , a family of subsets of
is -antichain saturated if it does not contain an antichain
of size , but adding any set to creates an antichain of size
. We use sat to denote the smallest size of such a family. For all
and sufficiently large , we determine the exact value of sat.
Our result implies that sat, which confirms
several conjectures on antichain saturation. Previously, exact values for
sat were only known for up to .
We also prove a generalisation of a result of Lehman-Ron which may be of
independent interest. We show that given disjoint chains in the Boolean
lattice, we can create disjoint skipless chains that cover the same
elements (where we call a chain skipless if any two consecutive elements differ
in size by exactly one).Comment: 29 pages, 3 figure
Efficient Bayesian Inference of General Gaussian Models on Large Phylogenetic Trees
Phylogenetic comparative methods correct for shared evolutionary history
among a set of non-independent organisms by modeling sample traits as arising
from a diffusion process along on the branches of a possibly unknown history.
To incorporate such uncertainty, we present a scalable Bayesian inference
framework under a general Gaussian trait evolution model that exploits
Hamiltonian Monte Carlo (HMC). HMC enables efficient sampling of the
constrained model parameters and takes advantage of the tree structure for fast
likelihood and gradient computations, yielding algorithmic complexity linear in
the number of observations. This approach encompasses a wide family of
stochastic processes, including the general Ornstein-Uhlenbeck (OU) process,
with possible missing data and measurement errors. We implement inference tools
for a biologically relevant subset of all these models into the BEAST
phylogenetic software package and develop model comparison through marginal
likelihood estimation. We apply our approach to study the morphological
evolution in the superfamilly of Musteloidea (including weasels and allies) as
well as the heritability of HIV virulence. This second problem furnishes a new
measure of evolutionary heritability that demonstrates its utility through a
targeted simulation study
Paneth cell - rich regions separated by a cluster of Lgr5+ cells initiate crypt fission in the intestinal stem cell niche
The crypts of the intestinal epithelium house the stem cells that ensure the continual renewal of the epithelial cells that line the intestinal tract. Crypt number increases by a process called crypt fission, the division of a single crypt into two daughter crypts. Fission drives normal tissue growth and maintenance. Correspondingly, it becomes less frequent in adulthood. Importantly, fission is reactivated to drive adenoma growth. The mechanisms governing fission are poorly understood. However, only by knowing how normal fission operates can cancer-associated changes be elucidated. We studied normal fission in tissue in three dimensions using high-resolution imaging and used intestinal organoids to identify underlying mechanisms. We discovered that both the number and relative position of Paneth cells and Lgr5+ cells are important for fission. Furthermore, the higher stiffness and increased adhesion of Paneth cells are involved in determining the site of fission. Formation of a cluster of Lgr5+ cells between at least two Paneth-cell-rich domains establishes the site for the upward invagination that initiates fission
Catolicismo e ciências sociais no Brasil: mudanças de foco e perspectiva num objeto de estudo
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