Some relational structures with polynomial growth and their associated algebras II: Finite generation

The profile of a relational structure $R$ is the function $\varphi_R$ which counts for every integer $n$ the number, possibly infinite, $\varphi_R(n)$ of substructures of $R$ induced on the $n$-element subsets, isomorphic substructures being identified. If $\varphi_R$ takes only finite values, this is the Hilbert function of a graded algebra associated with $R$, the age algebra $A(R)$, introduced by P.~J.~Cameron. In a previous paper, we studied the relationship between the properties of a relational structure and those of their algebra, particularly when the relational structure $R$ admits a finite monomorphic decomposition. This setting still encompasses well-studied graded commutative algebras like invariant rings of finite permutation groups, or the rings of quasi-symmetric polynomials. In this paper, we investigate how far the well know algebraic properties of those rings extend to age algebras. The main result is a combinatorial characterization of when the age algebra is finitely generated. In the special case of tournaments, we show that the age algebra is finitely generated if and only if the profile is bounded. We explore the Cohen-Macaulay property in the special case of invariants of permutation groupoids. Finally, we exhibit sufficient conditions on the relational structure that make naturally the age algebra into a Hopf algebra.Comment: 27 pages; submitte

Evidence for an interplay between cell cycle progression and the initiation of differentiation between life cycle forms of African trypanosomes

Successful transmission of the African trypanosome between the mammalian host blood-stream and the tsetse fly vector involves dramatic alterations in the parasite's morphology and biochemistry. This differentiation through to the tsetse midgut procyclic form is accompanied by re-entry into a proliferative cell cycle. Using a synchronous differentiation model and a variety of markers diagnostic for progress through both differentiation and the cell cycle, we have investigated the interplay between these two processes. Our results implicate a relationship between the trypanosome cell cycle position and the perception of the differentiation signal and demonstrate that irreversible commitment to the differentiation occurs rapidly after induction. Furthermore, we show that re-entry into the cell cycle in the differentiating population is synchronous, and that once initiated, progress through the differentiation pathway can be uncoupled from progress through the cell cycle

Heterogeneity and proliferation of invasive cancer subclones in game theory models of the Warburg effect

OBJECTIVES: The Warburg effect, the switch from aerobic energy production to anaerobic glycolysis, promotes tumour proliferation and motility by inducing acidification of the tumour microenvironment. Therapies that reduce acidity could impair tumour growth and invasiveness. I analyse the dynamics of cell proliferation and of resistance to therapies that target acidity in a population of cells under the Warburg effect. MATERIALS AND METHODS: The dynamics of mutant cells with increased glycolysis and motility is analysed in a multi-player game with collective interactions in the framework of evolutionary game theory. Perturbations of the level of acidity in the microenvironment are used to simulate the effect of therapies that target glycolysis. RESULTS: The non-linear effects of glycolysis induce frequency-dependent clonal selection leading to the coexistence of glycolytic and non-glycolytic cells within the tumour. Mutants with increased motility can invade such polymorphic population and spread within the tumour. While reducing acidity may produce a sudden reduction in tumour proliferation, frequency-dependent selection enables the tumour to adapt to the new conditions and can enable the tumour to restore the original levels of growth and invasiveness. CONCLUSIONS: The acidity produced by glycolysis acts as a non-linear public good that leads to the coexistence of cells with high and low glycolysis within the tumour. Such heterogeneous population can easily adapt to changes in acidity. Therapies that target acidity can only be effective in the long term if the cost of glycolysis is high, that is, under non-limiting oxygen concentrations. Their efficacy, therefore, is reduced when combined with therapies that impair angiogenesis

A parameterization process as a categorical construction

The parameterization process used in the symbolic computation systems Kenzo and EAT is studied here as a general construction in a categorical framework. This parameterization process starts from a given specification and builds a parameterized specification by transforming some operations into parameterized operations, which depend on one additional variable called the parameter. Given a model of the parameterized specification, each interpretation of the parameter, called an argument, provides a model of the given specification. Moreover, under some relevant terminality assumption, this correspondence between the arguments and the models of the given specification is a bijection. It is proved in this paper that the parameterization process is provided by a free functor and the subsequent parameter passing process by a natural transformation. Various categorical notions are used, mainly adjoint functors, pushouts and lax colimits

Evolutionary game theory

Game Theory

A Coalgebraic View on Reachability

Coalgebras for an endofunctor provide a category-theoretic framework for modeling a wide range of state-based systems of various types. We provide an iterative construction of the reachable part of a given pointed coalgebra that is inspired by and resembles the standard breadth-first search procedure to compute the reachable part of a graph. We also study coalgebras in Kleisli categories: for a functor extending a functor on the base category, we show that the reachable part of a given pointed coalgebra can be computed in that base category

Manifolds with non-stable fundamental groups at infinity, II

In this paper we continue an earlier study of ends non-compact manifolds. The over-arching goal is to investigate and obtain generalizations of Siebenmann's famous collaring theorem that may be applied to manifolds having non-stable fundamental group systems at infinity. In this paper we show that, for manifolds with compact boundary, the condition of inward tameness has substatial implications for the algebraic topology at infinity. In particular, every inward tame manifold with compact boundary has stable homology (in all dimensions) and semistable fundamental group at each of its ends. In contrast, we also construct examples of this sort which fail to have perfectly semistable fundamental group at infinity. In doing so, we exhibit the first known examples of open manifolds that are inward tame and have vanishing Wall finiteness obstruction at infinity, but are not pseudo-collarable.Comment: Published by Geometry and Topology at http://www.maths.warwick.ac.uk/gt/GTVol7/paper7.abs.htm