Constructing continuum many countable, primitive, unbalanced digraphs

AbstractWe construct continuum many non-isomorphic countable digraphs which are highly arc transitive, have finite out-valency and infinite in-valency, and whose automorphism groups are primitive

A matrix representation of graphs and its spectrum as a graph invariant

We use the line digraph construction to associate an orthogonal matrix with each graph. From this orthogonal matrix, we derive two further matrices. The spectrum of each of these three matrices is considered as a graph invariant. For the first two cases, we compute the spectrum explicitly and show that it is determined by the spectrum of the adjacency matrix of the original graph. We then show by computation that the isomorphism classes of many known families of strongly regular graphs (up to 64 vertices) are characterized by the spectrum of this matrix. We conjecture that this is always the case for strongly regular graphs and we show that the conjecture is not valid for general graphs. We verify that the smallest regular graphs which are not distinguished with our method are on 14 vertices.Comment: 14 page

Infinite primitive and distance transitive directed graphs of finite out-valency

We give certain properties which are satisfied by the descendant set of a vertex in an infinite, primitive, distance transitive digraph of finite out-valency and provide a strong structure theory for digraphs satisfying these properties. In particular, we show that there are only countably many possibilities for the isomorphism type of such a descendant set, thereby confirming a conjecture of the first Author. As a partial converse, we show that certain related conditions on a countable digraph are sufficient for it to occur as the descendant set of a primitive, distance transitive digraph

Rubisco is evolving for improved catalytic efficiency and CO2 assimilation in plants

Rubisco is the primary entry point for carbon into the biosphere. However, rubisco is widely regarded as inefficient leading many to question whether the enzyme can adapt to become a better catalyst. Through a phylogenetic investigation of the molecular and kinetic evolution of Form I rubisco we uncover the evolutionary trajectory of rubisco kinetic evolution in angiosperms. We show that rbcL is among the 1% of slowest-evolving genes and enzymes on Earth, accumulating one nucleotide substitution every 0.9 My and one amino acid mutation every 7.2 My. Despite this, rubisco catalysis has been continually evolving toward improved CO2/O2 specificity, carboxylase turnover, and carboxylation efficiency. Consistent with this kinetic adaptation, increased rubisco evolution has led to a concomitant improvement in leaf-level CO2 assimilation. Thus, rubisco has been slowly but continually evolving toward improved catalytic efficiency and CO2 assimilation in plants

Genetic analysis of historical human remains – what ancient bones can tell if one asks the right questions…

Poster presented at Genetics in Forensics, 14th-15th March 2016, London, United Kingdom

Target-driven investing: Optimal investment strategies in defined contribution pension plans under loss aversion

Assuming the loss aversion framework of Tversky and Kahneman (1992), stochastic investment and labour income processes, and a path-dependent fund target, we show that the optimal investment strategy for defined contribution pension plan members is a target-driven 'threshold' strategy, whereby the equity allocation is increased if the accumulating fund is below target and is decreased if it is above. However, if the fund is sufficiently above target, the optimal investment strategy switches to 'portfolio insurance'. We show that the risk of failing to attain the target replacement ratio is significantly lower with target-driven strategies than with those associated with the maximisation of expected utility

An alternative strategy for trypanosome survival in the mammalian bloodstream revealed through genome and transcriptome analysis of the ubiquitous bovine parasite Trypanosoma (Megatrypanum) theileri

There are hundreds of Trypanosoma species that live in the blood and tissue spaces of their vertebrate hosts. The vast majority of these do not have the ornate system of antigenic variation that has evolved in the small number of African trypanosome species, but can still maintain long term infections in the face of the vertebrate adaptive immune system. Trypanosoma theileri is a typical example, it has a restricted host range of cattle and other Bovinae and is only occasionally reported to cause patent disease although no systematic survey of the effect of infection on agricultural productivity has been performed. Here, a detailed genome sequence and a transcriptome analysis of gene expression in bloodstream form T. theileri have been performed. Analysis of the genome sequence and expression showed that T. theileri has a typical kinetoplastid genome structure and allowed a prediction that it is capable of meiotic exchange, gene silencing via RNA interference and, potentially, density-dependent growth control. In particular, the transcriptome analysis has allowed a comparison of two distinct trypanosome cell surfaces, T. brucei and T. theileri, that have each evolved to enable the maintenance of a long-term extracellular infection in cattle. The T. theileri cell surface can be modelled to contain a mixture of proteins encoded by four novel large and divergent gene families and by members of a major surface protease gene family. This surface composition is distinct from the uniform variant surface glycoprotein coat on African trypanosomes providing an insight into a second mechanism used by trypanosome species that proliferate in an extracellular milieu in vertebrate hosts to avoid the adaptive immune response

Age-dependent investing: Optimal funding and investment strategies in defined contribution pension plans when members are rational life cycle financial planners

A defined contribution pension plan allows consumption to be redistributed from the plan member's working life to retirement in a manner that is consistent with the member's personal preferences. The plan's optimal funding and investment strategies therefore depend on the desired profile of consumption over the lifetime of the member. We investigate these strategies under the assumption that the member is a rational life cycle financial planner and has an Epstein-Zin utility function, which allows a separation between risk aversion and the elasticity of intertemporal substitution. We also take into account the member's human capital during the accumulation phase of the plan and we allow the annuitisation decision to be endogenously determined during the decumulation phase. We show that the optimal funding strategy involves a contribution rate that is not constant over the life of the plan but is age-dependent and reflects the trade-off between the desire for current versus future consumption, the desire for stable consumption over time, the member's attitude to risk, and changes in the level of human capital over the life cycle. We also show that the optimal investment strategy during the accumulation phase of the plan is 'stochastic lifestyling', with an initial high weight in equity-type investments and a gradual switch into bond-type investments as the retirement date approaches in a way that depends on the realised outcomes for the stochastic processes driving the state variables. The optimal investment strategy during the decumulation phase of the plan is to exchange the bonds held at retirement for life annuities and then to gradually sell the remaining equities and buy more annuities, i.e., a strategy known as 'phased annuitisation'

Multi-tissue transcriptomes of caecilian amphibians highlight incomplete knowledge of vertebrate gene families

RNA sequencing (RNA-seq) has become one of the most powerful tools to unravel the genomic basis of biological adaptation & diversity. Although challenging, RNA-seq is particularly promising for research on non-model, secretive species that cannot be observed in nature easily and therefore remain comparatively understudied. Among such animals, the caecilians (order Gymnophiona) likely constitute the least known group of vertebrates, despite being an old and remarkably distinct lineage of amphibians. Here, we characterize multi-tissue transcriptomes for five species of caecilians that represent a broad level of diversity across the order. We identified vertebrate homologous elements of caecilian functional genes of varying tissue specificity that reveal a great number of unclassified gene families, especially for the skin. We annotated several protein domains for those unknown candidate gene families to investigate their function. We also conducted supertree analyses of a phylogenomic dataset of 1,955 candidate orthologous genes among five caecilian species and other major lineages of vertebrates, with the inferred tree being in agreement with current views of vertebrate evolution and systematics. Our study provides insights into the evolution of vertebrate protein-coding genes, and a basis for future research on the molecular elements underlying the particular biology and adaptations of caecilian amphibians

Evolutionary timeline and genomic plasticity underlying the lifestyle diversity in rhizobiales

Members of the order include those capable of nitrogen fixation in nodules as well as pathogens of animals and plants. This lifestyle diversity has important implications for agricultural and medical research. Leveraging large-scale genomic data, we infer that originated as a free-living ancestor ∼1,500 million years ago (Mya) and that the later emergence of host-associated lifestyles broadly coincided with the rise of their eukaryotic hosts. In particular, the first nodulating lineage arose from either or 150 to 80 Mya, a time range in general concurrent with the emergence of legumes. The rates of lifestyle transitions are highly variable; nodule association is more likely to be lost than gained, whereas animal association likely represents an evolutionary dead end. We searched for statistical correlations between gene presence and lifestyle and identified genes likely contributing to the transition and adaptation to the same lifestyle in divergent lineages. Among the genes potentially promoting successful transitions to major nodulation lineages, the and clusters for nodulation and nitrogen fixation, respectively, were repeatedly acquired during each transition; the , , and clusters involved in energy conservation under micro-oxic conditions were present in the nonnodulating ancestors; and the secretion systems were acquired in lineage-specific patterns. Our study data suggest that increased eukaryote diversity drives lifestyle diversification of bacteria and highlight both acquired and preexisting traits facilitating the origin of host association. Bacteria form diverse interactions with eukaryotic hosts. This is well represented by the , a clade of strategically important for their large diversity of lifestyles with implications for agricultural and medical research. To investigate their lifestyle evolution, we compiled a comprehensive data set of genomes and lifestyle information for over 1,000 genomes. We show that the origins of major host-associated lineages in broadly coincided with the emergences of their host plants/animals, suggesting bacterium-host interactions as a driving force in the evolution of We further found that, in addition to gene gains, preexisting traits and recurrent losses of specific genomic traits may have played underrecognized roles in the origin of host-associated lineages, providing clues to genetic engineering of microbial agricultural inoculants and prevention of the emergence of potential plant/animal pathogens