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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

RNA molecules are single-stranded analogues of DNA that can fold into various structures which influence their biological function within the cell. RNA structures can be modelled combinatorially in terms of a certain type of graph called an RNA diagram. In this paper we introduce a new poset of RNA diagrams $\mathcal{B}^r_{f,k}$, $r\ge 0$, $k \ge 1$ and $f \ge 3$, which we call the Penner-Waterman poset, and, using results from the theory of multitriangulations, we show that this is a pure poset of rank $k(2f-2k+1)+r-f-1$, whose geometric realization is the join of a simplicial sphere of dimension $k(f-2k)-1$ and an $\left((f+1)(k-1)-1\right)$-simplex in case $r=0$. As a corollary for the special case $k=1$, we obtain a result due to Penner and Waterman concerning the topology of the space of RNA secondary structures. These results could eventually lead to new ways to investigate landscapes of RNA $k$-noncrossing structures.

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.

We developed a method, ArchaicSeeker 2.0, to identify introgressed hominin sequences and model multiple-wave admixture. The new method enabled us to discern two waves of introgression from both Denisovan-like and Neanderthal-like hominins in present-day Eurasian populations and an ancient Siberian individual. We estimated that an early Denisovan-like introgression occurred in Eurasia around 118.8–94.0 thousand years ago (kya). In contrast, we detected only one single episode of Denisovan-like admixture in indigenous peoples eastern to the Wallace-Line. Modeling ancient admixtures suggested an early dispersal of modern humans throughout Asia before the Toba volcanic super-eruption 74 kya, predating the initial peopling of Asia as proposed by the traditional Out-of-Africa model. Survived archaic sequences are involved in various phenotypes including immune and body mass (e.g., ZNF169), cardiovascular and lung function (e.g., HHAT), UV response and carbohydrate metabolism (e.g., HYAL1/HYAL2/HYAL3), while “archaic deserts” are enriched with genes associated with skin development and keratinization., Existing methods to identify the presence of DNA from other hominin species can be limited in the ability to accurately estimate introgression waves, or can only be applied to specific populations. Here, the authors have developed a generalizable method to identify introgression in multi-wave situations.

Particulate matter (PM) emissions have become an increasingly noticeable concern for gasoline vehicles, especially for gasoline direct injection (GDI) one. The PM index (PMI) model developed by Aikiwa et al. provides an effective model linking the fuel properties to the PM emissions from gasoline vehicles. In this study, a more practical reduced PM index (RPMI) was developed based on the detailed analysis of 22 fuels with various physical properties and chemical compositions. Two approaches of statistical mathematics of correlation analysis and multivariate linear regression (MLR) were adopted in the modeling process. The RPMI involving two global fuel properties of T90 (distillation temperature of 90% by volume) and T70 (distillation temperature of 70% by volume) was tested to be statistically valid. In addition, the model was verified through the engine bench tests and the vehicle emissions tests. The results reveal that the RPMI showed good correlations to the engine-out particle number (PN) emissions under all of the typical test conditions, including PFI (port fuel injection) mode, GDI (gasoline direct injection) mode and compound injection (PFI + GDI) mode. In addition, the RPMI demonstrated a significantly high correlation to vehicle-out PN emissions over the New European Driving Cycle (NEDC) with the determination coefficient R2 = 0.947. Moreover, a moderate correlation (R2 = 0.801) of the index to the filter PM mass emissions was observed. In the light of no additional components analysis is needed except for the legitimate tests of fuels, the RPMI has the potential to be a useful tool for original equipment manufacturers (OEMs) and environmental certification departments to expediently evaluate the fuel effect on PM emissions.

Methanol is difficult to be ignited by compression due to its low cetane number. The strategy of diesel–methanol compound combustion (DMCC) was proposed, which starts up with pure diesel fuel and switches to the mode of diesel–methanol dual fuel after the engine fully warms up. The strategy of DMCC will substitute methanol to diesel fuel up to 40% for new engine and 30% for retrofitting engine when it is applied to heavy-duty vehicle and constructive machine as well as marine power unit. The engines equipped with DMCC system are able to reduce NOx without assistance of selective catalyst reduction (SCR) urea system, as well as PM emission at the same time, which can meet the requirements of China V emission legislation and have the potential to meet the demand of China VI in future. The chapter introduces the strategy of DMCC, the main components dealing with methanol while applied to those engines mentioned above, and real examples on different power units. Additionally, the characteristics of diesel–methanol dual fuel (DMDF) combustion mode, emission control strategy, and system related to catalyst, retrofitting, and modifying engine from pure diesel to running DMCC mode are also illustrated. Again, it provides with the research results about the characteristics of DMDF combustion mode to assist the readers to understand the dual fuel combustion in depth as well as the examples applied to various power units, such as heavy-duty trucks, constructive machine, marine propeller, and locomotive engines.

SUMMARYLymphocyte biology research commonly involves purification of lymphocyte subpopulations by fluorescence-activated cell sorting (FACS) or immunomagnetic separation (IMS), both of which typically rely on antibody labeling of validated cell markers. Methods enabling label-free segregation of lymphocyte subpopulations would be invaluable with regard to less-perturbation, simplicity and cost-effectiveness. Here, we introduce TRuST, a label-free approach forTcellreconstitutionusingside-scatter (SSC). TRuST-sorted SSClowcells enrich for CD4+T and naïve T cells, while SSChighcells enrich for CD8+T, NK and differentiated T cells. Enrichment purity can be improved by computational gate design. SSClowcells have superior expansion capacity and generate more central memory precursors with naïve-resembling cytokine responses. Moreover, we find that both T cell differentiation status and CD4/CD8 T ratio in the starting cellular material are critical attributes predicting T cell product quality and quantity. TRuST presents an effective and reliable technique for label-free lymphocytes selection and reconstitution.

The late-injection strategy (close after main-injection) of common-rail diesel engine is capable of enhancing combustion turbulence and reducing particulate matter (PM) emissions. In this work, experimental study was performed to investigate the effect of diesel late-injection on combustion and emissions characteristics of diesel/methanol dual fuel (DMDF) engine. The experiments were carried out at a constant engine speed of 1340 rpm and a medium load of 1.0 MPa brake mean effective pressure (BMEP) with various methanol substitution ratio (MSR) on a common rail DMDF engine. The results reveal that higher MSR caused simultaneous decrease of nitric oxides (NOx) and accumulation mode PM emissions in spite of late-injection strategy. In particular, an augment of up to 12.8% in nucleation mode particle number (PN) was observed as MSR increased from 15% to 50%. A small late-injection of diesel ( 1200 μs) induced a simultaneous increase of particles with different size.

UPGMA (Unweighted Pair Group Method with Arithmetic Mean) is a widely used clustering method. Here we show that UPGMA is a greedy heuristic for the normalized equidistant minimum evolution (NEME) problem, that is, finding a rooted tree that minimizes the minimum evolution score relative to the dissimilarity matrix among all rooted trees with the same leaf-set in which all leaves have the same distance to the root. We prove that the NEME problem is NP-hard. In addition, we present some heuristic and approximation algorithms for solving the NEME problem, including a polynomial time algorithm that yields a binary, rooted tree whose NEME score is within O(log^2 n) of the optimum. We expect that these results to eventually provide further insights into the behavior of the UPGMA algorithm., Comment: 29 pages, 8 figures

In this paper, an experimental investigation on achieving ultra-low raw emissions in a diesel/methanol dual fuel engine based on dual-loop EGR was carried out. The effect of dual-loop EGR (High pressure EGR and low pressure EGR) on the combustion, performance and emissions of methanol engine has been studied comprehensively. The results show that ultra-low NOx (

This paper explored the reason that the amount of methanol consumed is much lower than that of its theoretical value in terms of calorific value in diesel methanol dual fuel (DMDF) combustion by the means of engine bench test and modeling analysis. The results from experiments show that, the DMDF has much higher combustion rate than that of the correspondent diesel (D) mode and the accelerating effect caused by methanol changes with engine load, methanol-air mixture concentration and intake air temperature. At low load condition, the ignition delay caused by methanol is dominated while the accelerating effect is weak. However, this situation just turned upside down at high loads, to bring forth great improvement in isochoric degree. When methanol conducts quickly burning, both the combustion efficiency and the conversion efficiency from heat to work are improved, and the replacement ratio S R becomes much lower than its theoretical value 2.16. In order to reveal the mechanism of high efficiency DMDF at various running conditions, a 3-dimensional CFD model to simulate and analysis the process of methanol burning together with diesel was built. By fixing constant operating parameters and boundary conditions, both the putting off and accelerating effects caused by methanol are enhanced with increasing methanol concentration. The putting off effect weakens with rising air temperature, while the accelerating effect becomes more effective in this process. Hence, the isochoric degree for DMDF deteriorates with rising air temperature at lean methanol mixture but improves as the concentration increases. Finally, a relational graph among isochoric degree, heat release concentration degree, methanol-air mixture concentration and temperature are derived, from which we get the understanding of controllable methanol quick combustion (CMQC) to further improve the DMDF thermal efficiency.

Based on European Steady-state Cycle (ESC) test procedure, an engine test was carried out to meet the demand of Euro V legislation with diesel methanol compound combustion (DMCC) technology on a common-rail, turbocharged, inter-cooling heavy-duty and high pressure exhaust gas recirculation (HP EGR) diesel engine with meeting the requirements of Euro IV legislation. The engine was just modified with DMCC technology and combined with after-treatment device diesel oxidation catalyst coupled with particulate oxidation catalyst (DPOC). The test results show that it can fully meet the demand of Euro V legislation without the help of selected catalyst reduction (SCR). Additionally, the comparative analysis of the dynamic and economic performances between the DMCC Euro V engine and the baseline Euro IV engine was presented in this study. The regulated emissions (included HC, CO, NOX, PM (particulate matter)) and unregulated emissions (included formaldehyde (HCHO) and unburned methanol (CH3OH)) before and after DPOC from DMCC Euro V engine were also investigated. The dynamic performance of DMCC Euro V engine is basically consistent with the baseline Euro IV engine, while there is a slight deterioration in economic performance at certain operation conditions in terms of calorific value. Compared with the baseline engine before DPOC, the DMCC engine causes an increase in HC, CO, HCHO and CH3OH emissions, but the NOX and PM emissions are much better. The DPOC efficiency in the conversion rate of HC, CO, HCHO and CH3OH is over 98% under the whole ESC test procedure, and for PM, the conversion efficiency is only around 21%. However, DPOC has no obvious influence on the conversion of NOX emissions.

The increasing of fuel temperature can reduce the droplet size and have an advantage of improving spray atomization, while investigations of the effect of temperature on the methanol injector internal flow and external spray is rare. Firstly, a detailed three dimensional numerical simulations of nozzle internal flow have been conducted to probe into the cavitation in methanol injector nozzles, and then an experimental study has been carried out to investigate the droplet size and velocity of methanol spray at various temperatures using the Phase Doppler Particle Analyzer (PDPA) detecting system. And results show that the region of cavitations in nozzle orifice enlarges as methanol temperature and injection pressure increases, and the temperature for 'super-cavitation' occurring decreases gradually with the increasing of injection pressure. Moreover, the nozzle exit velocity, discharge coefficient and cavitations number were also analyzed. However, the discharge coefficient reduces nearly equal under various pressure when the methanol temperature is higher than 60 °C. In addition, the Sauter Mean Diameter (SMD) and velocity of methanol droplet were also analyzed, and found that the droplet velocity reaches the maximum value when the methanol temperature is 60 °C.

A diesel engine with 6-cylinder, turbocharged intercooling and common rail system was modified to operate on diesel/methanol dual fuel (DMDF). To optimize combustion process at high methanol substitution ratio (MSR) and further decrease exhaust emissions of DMDF engine at low load condition, pilot injection strategy was applied on it and the combustion, regulated and unregulated gaseous emission (included NOx, CO, THC, carbon dioxide (CO 2 ), nitrous oxide (N 2 O), unburned methanol (CH 3 OH), formaldehyde (HCHO), formic acid (HCOOH), 1,3-butadiene (1,3-C 4 H 6 ), benzene (C 6 H 6 ) and toluene (C 7 H 8 )) characteristics were experimentally investigated. Experimental results reveal that the application of pilot injection could improve combustion stability and fuel economy at high MSR, and it can also reduce regulated emissions CO, THC except NOx, and unregulated emissions tested in this study except CO 2 on M0 and M10 mode and toluene on M50 mode when compared with single injection cases. Increase pilot injection quantity and advance pilot injection timing both cause an increase in in-cylinder temperature and pressure before main combustion. The variations of pilot injection quantity and timing have less effect on regulated and unregulated gaseous emissions except NOx on M0 and M10 mode than higher MSR mode. With the rise of pilot quantity and the advance of pilot injection timing, HC and CO emissions decrease gradually but NOx emissions ascend; almost all unregulated emissions tested in this study on M30 mode reduce gradually; but when the MSR continues to rise to 50%, increasing emissions in unburned methanol, 1,3-butadiene and benzene are observed.

Diesel/natural gas dual fuel (DNDF) and diesel/methanol dual fuel (DMDF) both have very good potential for use in alternative energy technologies for internal combustion engine. In this work, a comparative study was done to better understand the ignition characteristics of dual fuel combustion. First, their apparent ignition characteristics were studied experimentally on a constant volume chamber and apparent ignition delay correlations of DNDF and DMDF were built; second, chemical kinetic analysis was used to explain the phenomenon observed; lastly, an improved KIVA-3 V code was applied to study the importance of the chemical interaction between diesel and methane or methanol on diesel ignition timing in an engine. Experimental results showed that both methanol and methane addition retarded the ignition of diesel and methane retarded less, which was due to the dehydrogenation of methanol and methane, reaction CH3 + HO2 = CH3O + OH and the formation of H2O2. CFD numerical results showed that, in the DMDF ...

The methanol fuel used in diesel engine can reduce the emissions effectively, while the performance of engine keeps unchanged or even improved, the study of methanol used in diesel engine is paid more and more attention. Experiments were conducted in a 4-cylinder, turbocharged direct injection diesel engine fueled with diesel/methanol dual fuel (DMDF). In the experiment, methanol was injected into inlet duct by two low-pressure injectors, and directly mixed with intake air before entering the engine. The diesel fuel was directly injected in cylinder. The methanol substitution percent (MSP), intake air temperature and engine speed were changed to investigate the unevenness degree (UED) cylinder-to-cylinder. The experimental results show that the UED of engine increases with the increase of MSP under various engine loads, the COV pp increases with MSP under low engine load, and the COV pp curves vary very little under low MSP under 75% and 100% engine load, but a significantly rise appeared when MSP further increases. The UED gradually increases with the increase of intake air temperature, and it is usually less than 8% when intake air temperatures lower than 80 °C under 40% MSP. It suggests it is helpful to decrease the UED when the intake air temperature is in the range of 35–80 °C as MSP less than 40%. In addition, the difference of pressure between cylinder-to-cylinder decreases with the increase of engine speed, it can be considered raising MSP at high engine speed in order to gain better engine economy.

An experimental study was conducted to investigate into the cyclic variations of diesel methanol dual fuel (DMDF) combustion on a methanol fumigated diesel engine. The effects of engine load, methanol substitution percent (MSP), injection timing and intake temperature on cyclic combustion variation were studied experimentally. In-cylinder pressure of 100 consecutive combustion cycles were recorded for each test case. The coefficient of variation (COV) of maximum in-cylinder pressure ( p max ), maximum mass-averaged temperature ( T max ) and the indicated mean effective pressure (IMEP) were used to evaluate the cyclic variations of DMDF combustion. The results showed that the stability of DMDF combustion at high loads is comparable with that of neat diesel combustion. But the magnitude of cyclic DMDF combustion variations increases at light loads and more sensitive to the quantity of fumigated methanol. At light loads, COV p max and COV T max increase significantly and the crank angles corresponding to p max and T max scatter more around with the increment of MSP. IMEP values show obvious fluctuations and are distributed in a wider range with an increase in MSP. DMDF combustion stability is very sensitive to intake temperature. At light loads the COVs of all combustion parameters decrease with the increment of intake temperature. In contrast, at high loads, the effect of intake temperature on the cyclic variations is quite small while there is a significant increase in the COVs when the intake temperature exceeds over 75 °C. Overall, injection timings does no effect on cyclic variations of DMDF combustion.

This paper presented the analytical results for the energy balance of a diesel methanol dual-fuel (DMDF) engine. A methanol injection system was fixed on a diesel engine and let the engine to alternate to run in either the pure diesel (D) mode or DMDF mode. Primary application of the thermal balance analysis was to investigate the cause of methanol replacement ratio SR changing with engine loads. Calculations were conducted within the control volume by comparing each of the energy terms. The results show that the reduction in cooling loss in DMDF mode is the dominant factor for low SR at high loads. While, a substantial increase in incomplete combustion loss in DMDF mode is the most important reason for high SR at low loads. Another application of the thermal balance analysis was to research the cooling loss in DMDF mode which implied unique characteristics. Therefore, the changing methanol replacement rate SP experiments were carried out in various engine loads, giving the results that the cooling loss in DMDF mode is always lower than that in D mode, and it goes even lower as SP rises. Finally, the effect of methanol temperature on SR was also investigated from the thermal balance point of view. The results reveal that the incomplete combustion loss decreasing in higher methanol temperature conditions will lead to a certain extent of SR drop. All these results are related to the energy flow distribution within the engine.

Diesel–methanol dual fuel (DMDF) engines at light loads suffer from low thermal efficiency and high unburned percentages of fuel. Pilot fuel injection timing and intake temperature are two important parameters which affect the combustion process in DMDF engines. In present experimental work, the combined effects of intake temperature and injection timing on the performance of a DMDF engine have been studied. The experiments were conducted on a methanol-fumigated diesel engine at 25% of full load and the results concerning performance, combustion characteristics and emissions were analyzed. Results show that the low efficiency at light loads can be improved significantly by raising the intake temperature and advancing the injection timing of direct-injected diesel. Increasing the intake temperature also significantly decreases the heat release rate of premixed combustion and increases the combustion rate of methanol burned by flame propagation. Flame propagation of the methanol–air mixture disappears gradually and DMDF combustion transforms into single stage combustion as the injection timing is retarded. When injection timing is retarded after 4.6° crank angle, misfire occurs at higher methanol substitute percent (MSP) and lower intake temperature, while the auto-ignition of methanol occurs at lower MSP and higher intake temperature. Under DMDF operation, soot and nitrogen oxides trade-off dilemma is completely broken at lower intake temperature and higher MSP.

Tandem duplication is a rearrangement process whereby a segment of DNA is replicated and proximally inserted. A sequence of these events is termed an evolution. Many different configurations can arise from such evolutions, generating some interesting combinatorial properties. Firstly, new DNA connections arising in an evolution can be algebraically represented with a word producing automaton. The number of words arising from n tandem duplications can then be recursively derived. Secondly, many distinct evolutions result in the same sequence of words. With the aid of a bi-colored 2d-tree, a Hasse diagram corresponding to a partially ordered set is constructed, for which the number of linear extensions equates to the number of evolutions generating a given word sequence. Thirdly, we implement some subtree prune and graft operations on this structure to show that the total number of possible evolutions arising from n tandem duplications is ? k = 1 n ( 4 k - ( 2 k + 1 ) ) . The space of structures arising from tandem duplication thus grows at a super-exponential rate with leading order term O ( 4 1 2 n 2 ) .

In order to reveal the mechanism of high thermal efficiency of diesel methanol dual fuel (DMDF) engine, the exergy loss of DMDF engine under different operating parameters is investigated by using experimental and calculative methods based on the second law of thermodynamics. It has been found that DMDF has lower heat transfer exergy loss under all engine loads due to the high latent heat of vaporization of methanol which reduces the temperature in-cylinder. The exhaust exergy loss of DMDF under high load is relatively low compared with that of pure diesel fuel, while it is opposite to that under medium-low load. This is due to the influence of different temperatures on the incomplete combustion of methanol, which also indicates the main cause for the high thermal efficiency of DMDF under high load. Then studies on exergy analysis of DMDF under different temperatures were carried out. The studies covers the effect of intake air temperature on exergy efficiency, the heat transfer exergy loss and the exhaust physical exergy loss increase with rising intake air temperature as well. The results shows that the exhaust chemical exergy loss decreases significantly with the increase of intake air temperature and higher intake air temperature helps to improve exergy efficiency. Additionally, it is concluded that higher methanol temperature and cooling water temperature can improve exergy efficiency by decreasing exhaust exergy loss and combustion irreversible exergy loss. Finally, some feasible measures are proposed to further improve DMDF engine’s performance.

In phylogenetics, a common strategy used to construct an evolutionary tree for a set of species $$X$$ is to search in the space of all such trees for one that optimizes some given score function (such as the minimum evolution, parsimony or likelihood score). As this can be computationally intensive, it was recently proposed to restrict such searches to the set of all those trees that are compatible with some circular ordering of the set $$X$$ . To inform the design of efficient algorithms to perform such searches, it is therefore of interest to find bounds for the number of trees compatible with a fixed ordering in the neighborhood of a tree that is determined by certain tree operations commonly used to search for trees: the nearest neighbor interchange (nni), the subtree prune and regraft (spr) and the tree bisection and reconnection (tbr) operations. We show that the size of such a neighborhood of a binary tree associated with the nni operation is independent of the tree’s topology, but that this is not the case for the spr and tbr operations. We also give tight upper and lower bounds for the size of the neighborhood of a binary tree for the spr and tbr operations and characterize those trees for which these bounds are attained.

Based on the first law of thermodynamics, this paper presents the experimental results of parameter study on energy balance of a diesel methanol dual fuel (DMDF) engine including load characteristic tests for both pure diesel (D) mode and DMDF mode and comparison of energy flow conversion under different load ratios. The results show that replacement ratio keeps decreasing with load increases. In addition, operating parameters, including cooling water temperature, intake air temperature and methanol temperature, were investigated to explore their effects on energy flow distribution in DMDF engine. The results show that increasing intake air temperature has the most important effect on reducing DMDF engine’ s replacement ratio. Besides that, higher cooling water temperature and methanol temperature also contribute to improving DMDF engine’s thermodynamics performance. All these phenomena can be explained by the energy flow transformation when switching to DMDF combustion. On the basis of the above analysis results, some feasible measurements are proposed to further improve DMDF engine’s thermodynamic behavior.

Evolutionary history of protein-protein interaction (PPI) networks provides valuable insight into molecular mechanisms of network growth. In this paper, we study how to infer the evolutionary history of a PPI network from its protein duplication relationship. We show that for a plausible evolutionary history of a PPI network, its relative quality, measured by the so-called loss number, is independent of the growth parameters of the network and can be computed efficiently. This finding leads us to propose two fast maximum likelihood algorithms to infer the evolutionary history of a PPI network given the duplication history of its proteins. Simulation studies demonstrated that our approach, which takes advantage of protein duplication information, outperforms NetArch, the first maximum likelihood algorithm for PPI network history reconstruction. Using the proposed method, we studied the topological change of the PPI networks of the yeast, fruitfly, and worm.

To any metric D on a finite set X, one can associate a metric space T(D) known as its tight span. Properties of T(D) often reveal salient properties of D. For example, cut sets of T(D), i.e., subsets of T(D) whose removal disconnect T(D), can help to identify clusters suggested by D and indicate how T(D) (and hence D) may be decomposed into simpler components. Given a bipartition or split S of X, we introduce in this paper a real-valued index @e"("D","S") that comes about by considering cut sets of T(D). We also show that this index is intimately related to another, more easily computable index @d"("D","S") whose definition does not directly depend on T(D). In addition, we provide an illustration for how these two new indices could help to extend and complement current distance-based methods for phylogenetic network construction such as split decomposition and NeighborNet.

Phylogenetic networks are a generalization of phylogenetic trees that allow for representation of reticulate evolution. Recently, a space of unrooted phylogenetic networks was introduced, where such a network is a connected graph in which every vertex has degree 1 or 3 and whose leaf-set is a fixed set $X$ of taxa. This space, denoted $\mathcal{N}(X)$, is defined in terms of two operations on networks -- the nearest neighbor interchange and triangle operations -- which can be used to transform any network with leaf set $X$ into any other network with that leaf set. In particular, it gives rise to a metric $d$ on $\mathcal N(X)$ which is given by the smallest number of operations required to transform one network in $\mathcal N(X)$ into another in $\mathcal N(X)$. The metric generalizes the well-known NNI-metric on phylogenetic trees which has been intensively studied in the literature. In this paper, we derive a bound for the metric $d$ as well as a related metric $d_{N\!N\!I}$ which arises when restricting $d$ to the subset of $\mathcal{N}(X)$ consisting of all networks with $2(|X|-1+i)$ vertices, $i \ge 1$. We also introduce two new metrics on networks -- the SPR and TBR metrics -- which generalize the metrics on phylogenetic trees with the same name and give bounds for these new metrics. We expect our results to eventually have applications to the development and understanding of network search algorithms., Comment: 17 pages, 5 figures. This version has a new figure to illustrate Lemma 3.2, and a new Corollary 5.7 that bounds the distance between networks in different tiers

In evolutionary biology, phylogenetic networks are constructed to represent the evolution of species in which reticulate events are thought to have occurred, such as recombination and hybridization. It is therefore useful to have efficiently computable metrics with which to systematically compare such networks. Through developing an optimal algorithm to enumerate all trinets displayed by a level-1 network (a type of network that is slightly more general than an evolutionary tree), here we propose a cubic-time algorithm to compute the trinet distance between two level-1 networks. Employing simulations, we also present a comparison between the trinet metric and the so-called Robinson-Foulds phylogenetic network metric restricted to level-1 networks. The algorithms described in this paper have been implemented in JAVA and are freely available at https://www.uea.ac.uk/computing/TriLoNet., Comment: 11pages, 5 figures

In this article we study the treewidth of the \emph{display graph}, an auxiliary graph structure obtained from the fusion of phylogenetic (i.e., evolutionary) trees at their leaves. Earlier work has shown that the treewidth of the display graph is bounded if the trees are in some formal sense topologically similar. Here we further expand upon this relationship. We analyse a number of reduction rules which are commonly used in the phylogenetics literature to obtain fixed parameter tractable algorithms. In some cases (the \emph{subtree} reduction) the reduction rules behave similarly with respect to treewidth, while others (the \emph{cluster} reduction) behave very differently, and the behaviour of the \emph{chain reduction} is particularly intriguing because of its link with graph separators and forbidden minors. We also show that the gap between treewidth and Tree Bisection and Reconnect (TBR) distance can be infinitely large, and that unlike, for example, planar graphs the treewidth of the display graph can be as much as linear in its number of vertices. On a slightly different note we show that if a display graph is formed from the fusion of a phylogenetic network and a tree, rather than from two trees, the treewidth of the display graph is bounded whenever the tree can be topologically embedded ("displayed") within the network. This opens the door to the formulation of the display problem in Monadic Second Order Logic (MSOL). A number of other auxiliary results are given. We conclude with a discussion and list a number of open problems., Comment: 29 pages, 12 figures

In this paper, we present a rigorous analysis on the limiting behavior of the degree distribution of the partial duplication model, a random network growth model in the duplication and divergence family that is popular in the study of biological networks. We show that for each non-negative integer k, the expected proportion of nodes of degree k approaches a limit as the network becomes large. This fills in a gap in previous studies. In addition, we prove that p=1/2, where p is the selection probability of the model, is the phase transition for the expected proportion of isolated nodes converging to 1, and hence answer a question raised in Bebek et al. [G. Bebek, P. Berenbrink, C. Cooper, T. Friedetzky, J. Nadeau, S.C. Sahinalp, The degree distribution of the generalized duplication model, Theoret. Comput. Sci. 369 (2006) 239-249]. We also obtain asymptotic bounds on the convergence rates of degree distribution. Since the observed networks typically do not contain isolated nodes, we study the subgraph consisting of all non-isolated nodes contained in the networks generated by the partial duplication model, and show that p=1/2 is again a phase transition for the limiting behavior of its degree distribution.

A realization of a finite metric space (X,d) is a weighted graph (G,w) whose vertex set contains X such that the distances between the elements of X in G correspond to those given by d. Such a realization is called optimal if it has minimal total edge weight. Optimal realizations have applications in fields such as phylogenetics, psychology, compression software and internet tomography. Given an optimal realization (G,w) of (X,d), there always exist certain ''proper'' maps from the vertex set of G into the so-called tight span of d. In [A. Dress, Trees, tight extensions of metric spaces, and the cohomological dimension of certain groups: a note on combinatorial properties of metric spaces, Adv. Math. 53 (1984) 321-402], Dress conjectured that any such map must be injective. Although this conjecture was recently disproven, in this paper we show that it is possible to characterize those optimal realizations (G,w) for which certain generalizations of proper maps-that map the geometric realization of (G,w) into the tight span instead of its vertex set-must always be injective. We also prove that these ''injective'' optimal realizations always exist, and show how they may be constructed from non-injective ones. Ultimately it is hoped that these results will contribute towards developing new ways to compute optimal realizations from tight spans.

A split system on a finite set X is a set of bipartitions of X. Weakly compatible and k-compatible (k≥1) split systems are split systems which satisfy special restrictions on all subsets of a certain fixed size. They arise in various areas of applied mathematics such as phylogenetics and multi-commodity flow theory. In this note, we show that the number of splits in a 3-compatible, weakly compatible split system on a set X of size n is linear in n.

We introduce the concept of single-linkage equivalence of edge-weighted graphs, we apply it to characterise maximal spanning trees and “ultra-similarities”, and we discuss how it relates to the popular single-linkage clustering algorithm.

In this paper we investigate guessing number, a relatively new concept linked to network coding and certain long standing open questions in circuit complexity. Here we study the bounds and a variety of properties concerning this parameter. As an application, we obtain the lower and upper bounds for shift graphs, a subclass of directed circulant graphs.

We investigate the computational complexity of finding an element of a permutation group [email protected]?S"n with minimal distance to a given @[email protected]?S"n, for different metrics on S"n. We assume that H is given by a set of generators. In particular, the size of H might be exponential in the input size, so that in general the problem cannot be solved in polynomial time by exhaustive enumeration. For the case of the Cayley Distance, this problem has been shown to be NP-hard, even if H is abelian of exponent two [R.G.E. Pinch, The distance of a permutation from a subgroup of S"n, in: G. Brightwell, I. Leader, A. Scott, A. Thomason (Eds.), Combinatorics and Probability, Cambridge University Press, 2007, pp. 473-479]. We present a much simpler proof for this result, which also works for the Hamming Distance, the l"p distance, Lee's Distance, Kendall's tau, and Ulam's Distance. Moreover, we give an NP-hardness proof for the l"~ distance using a different reduction idea. Finally, we discuss the complexity of the corresponding fixed-parameter and maximization problems.

Given a metric d on a permutation group G, the corresponding weight problem is to decide whether there exists an element g ∈ G such that d( g , e) = k for some k ∈ N . In this paper we show that this problem is NP-complete for many well known metrics.

Motivation: Distance methods are well suited for constructing massive phylogenetic trees. However, the computational complexity for Rzhetsky and Nei’s minimum evolution (ME) approach, one of the earliest methods for constructing a phylogenetic tree from a distance matrix, remains open. Results: We show that Rzhetsky and Nei’s ME problem is NP-complete, and so probably computationally intractable. We do this by linking the ME problem to a graph clustering problem called the quasi-clique decomposition problem, which has recently also been shown to be NP-complete. We also discuss how this link could potentially open up some useful new connections between phylogenetics and graph clustering. Contact: taoyang.wu@uea.ac.uk Supplementary information: Supplementary data are available at Bioinformatics online.

In phylogenetics, distances are often used to measure the incongruence between a pair of phylogenetic trees that are reconstructed by different methods or using different regions of genome. Motivated by the maximum parsimony principle in tree inference, we recently introduced the maximum parsimony (MP) distance, which enjoys various attractive properties due to its connection with several other well-known tree distances, such as TBR and SPR. Here we show that computing the MP distance between two trees, a NP-hard problem in general, is fixed parameter tractable in terms of the TBR distance between the tree pair. Our approach is based on two reduction rules--the chain reduction and the subtree reduction--that are widely used in computing TBR and SPR distances. More precisely, we show that reducing chains to length 4 (but not shorter) preserves the MP distance. In addition, we describe a generalization of the subtree reduction which allows the pendant subtrees to be rooted in different places, and show that this still preserves the MP distance. On a slightly different note we also show that Monadic Second Order Logic (MSOL), posited over an auxiliary graph structure known as the display graph (obtained by merging the two trees at their leaves), can be used to obtain an alternative proof that computation of MP distance is fixed parameter tractable in terms of TBR-distance. We conclude with an extended discussion in which we focus on similarities and differences between MP distance and TBR distance and present a number of open problems. One particularly intriguing question, emerging from the MSOL formulation, is whether two trees with bounded MP distance induce display graphs of bounded treewidth., Comment: Added material on graph minors, MSOL and treewidth

Phylogenetic networks are a generalization of evolutionary or phylogenetic trees that are used to represent the evolution of species which have undergone reticulate evolution. In this paper we consider spaces of such networks defined by some novel local operations that we introduce for converting one phylogenetic network into another. These operations are modeled on the well-studied nearest-neighbor interchange (NNI) operations on phylogenetic trees, and lead to natural generalizations of the tree spaces that have been previously associated to such operations. We present several results on spaces of some relatively simple networks, called level-1 networks, including the size of the neighborhood of a fixed network, and bounds on the diameter of the metric defined by taking the smallest number of operations required to convert one network into another.We expect that our results will be useful in the development of methods for systematically searching for optimal phylogenetic networks using, for example, likelihood and Bayesian approaches.

The Yule-Harding-Kingman (YHK) model and the proportional to distinguishable arrangements (PDA) model are two binary tree generating models that are widely used in evolutionary biology. Understanding the distributions of clade sizes under these two models provides valuable insights into macro-evolutionary processes, and is important in hypothesis testing and Bayesian analyses in phylogenetics. Here we show that these distributions are log-convex, which implies that very large clades or very small clades are more likely to occur under these two models. Moreover, we prove that there exists a critical value $\kappa(n)$ for each $n\geqslant 4$ such that for a given clade with size $k$, the probability that this clade is contained in a random tree with $n$ leaves generated under the YHK model is higher than that under the PDA model if $1, Comment: 21pages

Tree rearrangement operations typically induce a metric on the space of phylogenetic trees. One important property of these metrics is the size of the neighborhood, that is, the number of trees exactly one operation from a given tree. We present an exact expression for the size of the TBR (tree bisection and reconnection) neighborhood, thus answering a question first posed by Allen and Steel . In addition, we also obtain a characterization of the extremal trees whose TBR neighborhoods are maximized and minimized.

Tree reconciliation approach to inferring the duplication history for a gene family poses challenging problems when input gene and species trees are non-binary. We present the first linear-time algorithm that outputs a reconciliation of a non-binary gene tree and a binary species tree that minimizes the gene loss cost under the constraint of having the smallest gene duplication cost. As a part of a method for reconciling two non-binary trees, this algorithm has been implemented in a software package (http://phylotoo.appspot.com).

Genome-wide protein-protein interaction (PPI) data are readily available thanks to recent breakthroughs in biotechnology. However, PPI networks of extant organisms are only snapshots of the network evolution. How to infer the whole evolution history becomes a challenging problem in computational biology. In this paper, we present a likelihood-based approach to inferring network evolution history from the topology of PPI networks and the duplication relationship among the paralogs. Simulations show that our approach outperforms the existing ones in terms of the accuracy of reconstruction. Moreover, the growth parameters of several real PPI networks estimated by our method are more consistent with the ones predicted in literature.

Introduction A gene tree for a gene family is often discordant with the containing species tree because of its complex evolutionary course during which gene duplication, gene loss and incomplete lineage sorting events might occur. Hence, it is of great challenge to infer the containing species tree from a set of gene trees. One common approach to this inference problem is through gene tree and species tree reconciliation. Results In this paper, we generalize the traditional least common ancestor (LCA) reconciliation to define a reconciliation between a gene tree and species tree under the tree homomorphism framework. We then study the structural properties of the space of all reconciliations between a gene tree and a species tree in terms of the gene duplication, gene loss or deep coalescence costs. As application, we show that the LCA reconciliation is the unique one that has the minimum deep coalescence cost, provide a novel characterization of the reconciliations with the optimal duplication cost, and present efficient algorithms for enumerating (nearly-)optimal reconciliations with respect to each cost. Conclusions This work provides a new graph-theoretic framework for studying gene tree and species tree reconciliations.

Background: Horizontal gene transfer and gene duplication are two significant forces behind genome evolution. As more and more well-supported examples of HGTs are being revealed, there is a growing awareness that HGT is more widespread than previously thought, occurring often not only within bacteria, but also between species remotely related such as bacteria and plants or plants and animals. Although a substantial number of genomic sequences are known, HGT inference remains challenging. Parsimony-based inferences of HGT events are typically NP-hard under the framework of gene tree and species tree comparison; it is even more timeconsuming if the maximum likelihood approach is used. The fact that gene tree and species tree incongruence can be further confounded by gene duplication and gene loss events motivates us to incorporate considerations for these events into our inference of HGT events. Similarly, it will be beneficial if known HGT events are considered in the inference of gene duplications and gene losses.

A hierarchical structure describing the inter-relationships of species has long been a fundamental concept in systematic biology, from Linnean classification through to the more recent quest for a ‘Tree of Life’. In this paper we use an approach based on discrete mathematics to address a basic question: could one delineate this hierarchical structure in nature purely by reference to the ‘genealogy’ of present-day individuals, which describes how they are related with one another by ancestry through a continuous line of descent? We describe several mathematically precise ways by which one can naturally define collections of subsets of present day individuals so that these subsets are nested (and so form a tree) based purely on the directed graph that describes the ancestry of these individuals. We also explore the relationship between these and related clustering constructions.

Given a set X of taxa, a phylogenetic X-tree T that is only partially resolved, and a collection of characters on X, we consider the problem of finding a resolution (refinement) of T that minimizes the parsimony score of the given characters. Previous work has shown that this problem has a polynomial time solution provided certain strong constraints are imposed on the input. In this paper we provide a new algorithm for this problem, and show that it is fixed parameter tractable under more general conditions.