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We study two fringe subtree counting statistics, the number of cherries and that of pitchforks for Ford's $\alpha$ model, a one-parameter family of random phylogenetic tree models that includes the uniform and the Yule models, two tree models commonly used in phylogenetics. Based on a nonuniform version of the extended P\'olya urn models in which negative entries are permitted for their replacement matrices, we obtain the strong law of large numbers and the central limit theorem for the joint distribution of these two count statistics for the Ford model. Furthermore, we derive a recursive formula for computing the exact joint distribution of these two statistics. This leads to exact formulas for their means and higher order asymptotic expansions of their second moments, which allows us to identify a critical parameter value for the correlation between these two statistics. That is, when $n$ is sufficiently large, they are negatively correlated for $0\le \alpha \le 1/2$ and positively correlated for $1/2, Comment: 23 pages, 2 figures

SUMMARYCalcium signalling is central to many plant processes, with families of calcium decoder proteins having expanded across the green lineage and redundancy existing between decoders. The liverwort Marchantia polymorpha has fast become a new model plant, but it is unclear what calcium decoders exist in this species.We have performed phylogenetic analyses to identify the Calcineurin B-Like (CBL) and CBL-Interacting Protein Kinase (CIPK) network of M. polymorpha. We analysed CBL-CIPK expression during salt stress, and determined protein-protein interactions using yeast two-hybrid and bimolecular fluorescence complementation. We also created genetic knockouts using CRISPR/Cas9.We confirm that M. polymorpha has two CIPKs and three CBLs. Both CIPKs and only one CBL show salt-responsive transcriptional changes. All M. polymorpha CBL-CIPKs interact with each other in planta. Knocking out CIPK-B causes increased sensitivity to salt suggesting that this CIPK is involved in salt signalling.We have identified CBL-CIPKs that form part of a salt tolerance pathway in M. polymorpha. Phylogeny and interaction studies imply that these CBL-CIPKs form an evolutionarily conserved Salt Overly Sensitive (SOS) pathway. Hence, salt responses may be some of the early functions of CBL-CIPK networks and increased abiotic stress tolerance required for land plant emergence.

In order to reduce the pollutant emission and alleviate the pressure of petroleum resources shortage and greenhouse gas emission at the same time, the use of clean and renewable alternative fuel for marine engines is a promising option. In this study, a marine diesel engine, which was modified to run in diesel methanol compound combustion (DMCC) mode, was investigated. After the diesel injection parameters were calibrated, and combined with a sample after-treatment device DOC (diesel oxidation catalyst), the engine could meet the requirements of China II legislation. The overall MSP (methanol substitute percent) reached 54.1%. The value of each pollutant emission was much lower than that in China II emission legislation, and there was almost no methanol and formaldehyde emissions. When methanol was injected into the inlet manifold, the intake air temperature decreased a lot, as well as the exhaust gas temperature, which were beneficial to increase engine thermal efficiency and improve engine room environment. Compared with the engine running in pure diesel mode, when the engine ran in diesel/methanol dual fuel mode, the combustion phase was advanced, and the combustion duration became shorter. Therefore, the engine thermal efficiency increased, and fuel consumption decreased significantly.

A rooted phylogenetic network is a directed acyclic graph with a single root, whose sinks correspond to a set of species. As such networks are useful for representing the evolution of species that have undergone reticulate evolution, there has been great interest in developing the theory behind and algorithms for constructing them. However, unlike evolutionary trees, these networks can be highly non-planar, which can make them difficult to visualise and interpret. Here we investigate properties of planar rooted phylogenetic networks and algorithms for deciding whether or not rooted networks have certain special planarity properties. In particular, we introduce three natural subclasses of planar rooted phylogenetic networks and show that they form a hierarchy. In addition, for the well-known level-k networks, we show that level-1, -2, -3 networks are always outer, terminal, and upward planar, respectively, and that level-4 networks are not necessarily planar. Finally, we show that a regular network is terminal planar if and only if it is pyramidal. Our results make use of the highly developed field of planar digraphs, and we believe that the link between phylogenetic networks and planar graphs should prove useful in future for developing new approaches to both construct and visualise phylogenetic networks., 11 pages