Graph burning is a discrete time process which can be used to model the spread of social contagion. One is initially given a graph of unburned vertices. At each round (time step), one vertex is ...burned; unburned vertices with at least one burned neighbour from the previous round also becomes burned. The burning number of a graph is the fewest number of rounds required to burn the graph. It has been conjectured that for a graph on
n
vertices, the burning number is at most
⌈
n
⌉
. We show that the graph burning conjecture is true for trees without degree-2 vertices.
Phylogenetic networks are used in biology to represent evolutionary histories. The class of orchard phylogenetic networks was recently introduced for their computational benefits, without any ...biological justification. Here, we show that orchard networks can be interpreted as trees with additional
horizontal
arcs. Therefore, they are closely related to tree-based networks, where the difference is that in tree-based networks the additional arcs do not need to be horizontal. Then, we use this new characterization to show that the space of orchard networks on
n
leaves with
k
reticulations is connected under the rNNI rearrangement move with diameter
O
(
k
n
+
n
log
(
n
)
)
.
We present the first fixed-parameter algorithm for constructing a tree-child phylogenetic network that displays an arbitrary number of binary input trees and has the minimum number of reticulations ...among all such networks. The algorithm uses the recently introduced framework of cherry picking sequences and runs in
O
(
(
8
k
)
k
poly
(
n
,
t
)
)
time, where
n
is the number of leaves of every tree,
t
is the number of trees, and
k
is the reticulation number of the constructed network. Moreover, we provide an efficient parallel implementation of the algorithm and show that it can deal with up to 100 input trees on a standard desktop computer, thereby providing a major improvement over previous phylogenetic network construction methods.
Phylogenetic networks can represent evolutionary events that cannot be described by phylogenetic trees. These networks are able to incorporate reticulate evolutionary events such as hybridization, ...introgression, and lateral gene transfer. Recently, network-based Markov models of DNA sequence evolution have been introduced along with model-based methods for reconstructing phylogenetic networks. For these methods to be consistent, the network parameter needs to be identifiable from data generated under the model. Here, we show that the semi-directed network parameter of a triangle-free, level-1 network model with any fixed number of reticulation vertices is generically identifiable under the Jukes–Cantor, Kimura 2-parameter, or Kimura 3-parameter constraints.
Phylogenetic networks are used to represent evolutionary scenarios in biology and linguistics. To find the most probable scenario, it may be necessary to compare candidate networks. In particular, ...one needs to distinguish different networks and determine whether one network is contained in another. In this paper, we introduce cherry-picking networks, a class of networks that can be reduced by a so-called cherry-picking sequence. We then show how to compare such networks using their sequences. We characterize reconstructible cherry-picking networks, which are the networks that are uniquely determined by the sequences that reduce them, making them distinguishable. Furthermore, we show that a cherry-picking network is contained in another cherry picking network if a sequence for the latter network reduces the former network, provided both networks can be reconstructed from their sequences in a similar way (i.e., they are in the same reconstructible class). Lastly, we show that the converse of the above statement holds for tree-child networks, thereby showing that Network Containment, the problem of checking whether a network is contained in another, can be solved by computing cherry picking sequences in linear time for tree-child networks.
During the Fukushima Daiichi Nuclear Power Plant accident occurred in 2011, volatile fission products (FPs) such as Cs and I had released and caused environmental contamination and public exposure, ...respectively. However, the release mechanism of these FPs from fuels under the accident is still not completely understood. In recent years, we have focused on the wettability of liquid FPs against solid fuels, because the interface between the fuel surface and the FPs becomes the migration pathway, which might have large influences on the release behaviour of the FPs. Here, we studied the wettability of liquid CsI and B
2
O
3
on yttria-stabilized zirconia (YSZ) solid surface by the sessile drop test, where YSZ is a simulated material of the fuel. It was revealed that liquid CsI exhibited extremely high wettability against the YSZ surface with the contact angle of nearly zero. This high wettability may act to suppress the FPs release. Furthermore, it was confirmed that the crystal orientation and surface roughness of the YSZ solids have large influences on the wettability of liquid B
2
O
3
. The present results contribute for deep understanding of the release behaviour of the volatile FPs from fuels.
Polynomial invariants for cactuses van Iersel, Leo; Moulton, Vincent; Murakami, Yukihiro
Information processing letters,
August 2023, 2023-08-00, Letnik:
182
Journal Article
Recenzirano
Odprti dostop
Graph invariants are a useful tool in graph theory. Not only do they encode useful information about the graphs to which they are associated, but complete invariants can be used to distinguish ...between non-isomorphic graphs. Polynomial invariants for graphs such as the well-known Tutte polynomial have been studied for several years, and recently there has been interest to also define such invariants for phylogenetic networks, a special type of graph that arises in the area of evolutionary biology. Recently Liu gave a complete invariant for (phylogenetic) trees. However, the polynomial invariants defined thus far for phylogenetic networks that are not trees require vertex labels and either contain a large number of variables, or they have exponentially many terms in the number of reticulations. This can make it difficult to compute these polynomials and to use them to analyse unlabelled networks. In this paper, we shall show how to circumvent some of these difficulties for rooted cactuses and cactuses. As well as being important in other areas such as operations research, rooted cactuses contain some common classes of phylogenetic networks such phylogenetic trees and level-1 networks. More specifically, we define a polynomial F that is a complete invariant for the class of rooted cactuses without vertices of indegree 1 and outdegree 1 that has 5 variables, and a polynomial Q that is a complete invariant for the class of rooted cactuses that has 6 variables whose degree can be bounded linearly in terms of the size of the rooted cactus. We also explain how to extend the Q polynomial to define a complete invariant for leaf-labelled rooted cactuses as well as (unrooted) cactuses.
•We introduce a complete polynomial invariant for rooted cactuses.•This invariant can be used to encode rooted cactuses, which can be used in the comparison of phylogenetic networks.•We extend the invariant to give a complete polynomial invariant for undirected cactuses and to leaf-labelled rooted cactuses.
Degradable vinyl polymers are synthesized with periodically arranged in‐chain thioacetal bonds via cationic degenerative chain‐transfer copolymerization of vinyl ethers with a seven‐membered cyclic ...thioacetal, as reported by Mineto Uchiyama, Masami Kamigaito, and co‐workers in their Research Article (e202215021). The copolymers can be degraded into low‐ and controlled‐molecular‐weight polymers via hydrolysis.
A phylogenetic network is a graph-theoretical tool that is used by biologists to represent the evolutionary history of a collection of species. One potential way of constructing such networks is via ...a distance-based approach, where one is asked to find a phylogenetic network that in some way represents a given distance matrix, which gives information on the evolutionary distances between present-day taxa. Here, we consider the following question. For which k are unrooted level-k networks uniquely determined by their distance matrices? We consider this question for shortest distances as well as for the case that the multisets of all distances is given. We prove that level-1 networks and level-2 networks are reconstructible from their shortest distances and multisets of distances, respectively. Furthermore we show that, in general, networks of level higher than 1 are not reconstructible from shortest distances and that networks of level higher than 2 are not reconstructible from their multisets of distances.
PDF
