5,970 research outputs found
A 'stochastic safety radius' for distance-based tree reconstruction
A variety of algorithms have been proposed for reconstructing trees that show
the evolutionary relationships between species by comparing differences in
genetic data across present-day taxa. If the leaf-to-leaf distances in a tree
can be accurately estimated, then it is possible to reconstruct this tree from
these estimated distances, using polynomial-time methods such as the popular
`Neighbor-Joining' algorithm. There is a precise combinatorial condition under
which distance-based methods are guaranteed to return a correct tree (in full
or in part) based on the requirement that the input distances all lie within
some `safety radius' of the true distances. Here, we explore a stochastic
analogue of this condition, and mathematically establish upper and lower bounds
on this `stochastic safety radius' for distance-based tree reconstruction
methods. Using simulations, we show how this notion provides a new way to
compare the performance of distance-based tree reconstruction methods. This may
help explain why Neighbor-Joining performs so well, as its stochastic safety
radius appears close to optimal (while its more classical safety radius is the
same as many other less accurate methods).Comment: 18 pages, 1 figure, 4 table
Tracing evolutionary links between species
The idea that all life on earth traces back to a common beginning dates back
at least to Charles Darwin's {\em Origin of Species}. Ever since, biologists
have tried to piece together parts of this `tree of life' based on what we can
observe today: fossils, and the evolutionary signal that is present in the
genomes and phenotypes of different organisms. Mathematics has played a key
role in helping transform genetic data into phylogenetic (evolutionary) trees
and networks. Here, I will explain some of the central concepts and basic
results in phylogenetics, which benefit from several branches of mathematics,
including combinatorics, probability and algebra.Comment: 18 pages, 6 figures (Invited review paper (draft version) for AMM
Autonomous 3D Exploration of Large Structures Using an UAV Equipped with a 2D LIDAR
This paper addressed the challenge of exploring large, unknown, and unstructured
industrial environments with an unmanned aerial vehicle (UAV). The resulting system combined
well-known components and techniques with a new manoeuvre to use a low-cost 2D laser to measure
a 3D structure. Our approach combined frontier-based exploration, the Lazy Theta* path planner, and
a flyby sampling manoeuvre to create a 3D map of large scenarios. One of the novelties of our system
is that all the algorithms relied on the multi-resolution of the octomap for the world representation.
We used a Hardware-in-the-Loop (HitL) simulation environment to collect accurate measurements
of the capability of the open-source system to run online and on-board the UAV in real-time. Our
approach is compared to different reference heuristics under this simulation environment showing
better performance in regards to the amount of explored space. With the proposed approach, the UAV
is able to explore 93% of the search space under 30 min, generating a path without repetition that
adjusts to the occupied space covering indoor locations, irregular structures, and suspended obstaclesUnión Europea Marie Sklodowska-Curie 64215Unión Europea MULTIDRONE (H2020-ICT-731667)Uniión Europea HYFLIERS (H2020-ICT-779411
Statistical characterization and reconstruction of heterogeneous microstructures using deep neural network
Heterogeneous materials, whether natural or artificial, are usually composed of distinct constituents present in complex microstructures with discontinuous, irregular and hierarchical characteristics. For many heterogeneous materials, such as porous media and composites, the microstructural features are of fundamental importance for their macroscopic properties. This paper presents a novel method to statistically characterize and reconstruct random microstructures through a deep neural network (DNN) model, which can be used to study the microstructure–property relationships. In our method, the digital microstructure image is assumed to be a stationary Markov random field (MRF), and local patterns covering the basic morphological features are collected to train a DNN model, after which statistically equivalent samples can be generated through a DNN-guided reconstruction procedure. Furthermore, to overcome the short-distance limitation associated with the MRF assumption, a multi-level approach is developed to preserve the long-distance morphological features of heterogeneous microstructures. A large number of tests have been conducted to compare the reconstructed and target microstructures in both morphological characteristics and physical properties, and good agreements are observed in all test cases. The proposed method is efficient, accurate, versatile, and especially beneficial to the statistical reconstruction of 2D/3D microstructures with long-distance correlations
Efficiency of Algorithms in Phylogenetics
Phylogenetics is the study of evolutionary relationships between species. Phylogenetic
trees have long been the standard object used in evolutionary biology to illustrate how a
given set of species are related. There are some groups (including certain plant and fish
species) for which the ancestral history contains reticulation events, caused by processes that
include hybridization, lateral gene transfer, and recombination. For such groups of species, it
is appropriate to represent their ancestral history by phylogenetic networks: rooted acyclic
digraphs, where arcs represent lines of genetic inheritance and vertices of in-degree at least
two represent reticulation events. This thesis is concerned with the efficiency, accuracy, and
tractability of mathematical models for phylogenetic network methods.
Three important and related measures for summarizing the dissimilarity in phylogenetic
trees are the minimum number of hybridization events required to fit two phylogenetic trees
onto a single phylogenetic network (the hybridization number), the (rooted) subtree prune
and regraft distance (the rSPR distance) and the tree bisection and reconnection distance (the
TBR distance) between two phylogenetic trees. The respective problems of computing these
measures are known to be NP-hard, but also fixed-parameter tractable in their respective
natural parameters. This means that, while they are hard to compute in general, for cases
in which a parameter (here the hybridization number and rSPR/TBR distance, respectively)
is small, the problem can be solved efficiently even for large input trees. Here, we present
new analyses showing that the use of the “cluster reduction” rule – already defined for the
hybridization number and the rSPR distance and introduced here for the TBR distance – can
transform any O(f(p) · n)-time algorithm for any of these problems into an O(f(k) · n)-time
one, where n is the number of leaves of the phylogenetic trees, p is the natural parameter
and k is a much stronger (that is, smaller) parameter: the minimum level of a phylogenetic
network displaying both trees. These results appear in [9].
Traditional “distance based methods” reconstruct a phylogenetic tree from a matrix of pairwise
distances between taxa. A phylogenetic network is a generalization of a phylogenetic
tree that can describe evolutionary events such as reticulation and hybridization that are not
tree-like. Although evolution has been known to be more accurately modelled by a network
than a tree for some time, only recently have efforts been made to directly reconstruct a
phylogenetic network from sequence data, as opposed to reconstructing several trees first and then trying to combine them into a single coherent network. In this work, we present
a generalisation of the UPGMA algorithm for ultrametric tree reconstruction which can
accurately reconstruct ultrametric tree-child networks from the set of distinct distances
between each pair of taxa. This result will also appear in [15]. Moreover, we analyse the
safety radius of the NETWORKUPGMA algorithm and show that it has safety radius 1/2.
This means that if we can obtain accurate estimates of the set of distances between each pair
of taxa in an ultrametric tree-child network, then NETWORKUPGMA correctly reconstructs
the true network
Technical Design Report for PANDA Electromagnetic Calorimeter (EMC)
This document presents the technical layout and the envisaged performance of the Electromagnetic Calorimeter (EMC) for the
PANDA target spectrometer. The EMC has been designed to meet the physics goals of the PANDA experiment. The performance figures are based on extensive prototype tests and radiation hardness studies. The document shows that the EMC is ready for construction up to the front-end electronics interface
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