Genet age in marginal populations of two clonal Carex species in the Siberian Arctic

During a Swedish-Russian expedition to northern Siberia 1994, we sampled two marginal populations of two Carex species at two high arctic sites (C. stuns Drej. on Faddeyevsky Island and C. ensifolia V. Krecz ssp, arctisibirica Jurtz. at north-eastern Taymyr Peninsula), both north of previously documented localities in that areas for the two species. These populations were composed of a few distinct patches of ramet colonies, some of them shaped like fairy rings with dead centres. We measured the size of all colonies and collected samples for detailed morphometric analyses of rhizome growth. By using RAPD (random amplified polymorphic DNA) analysis we established that the largest colony at each site consisted of a single genet, based on 41 polymorphic bands amplified with three primers. Fouled samples from each of two additional colonies of C. stuns on Faddeyevsky Island were analysed and showed that clones of the same species at the same site were relatively dissimilar (Dice's similarity index 0.26-0.43). We then assumed that each ramet colony represented a single genet. Based on the morphometric data, we developed a deterministic growth model that simulates the clonal growth of these species and enabled estimates of the time since establishment of the genets. The estimated age of the five C. stans clones varied from 17 to 154 yr and the age of the two C. ensifolia ssp. arctisibirica clones was well over 3000 yr

Almost clean rings and arithmetical rings

It is shown that a commutative B\'ezout ring $R$ with compact minimal prime spectrum is an elementary divisor ring if and only if so is $R/L$ for each minimal prime ideal $L$. This result is obtained by using the quotient space $\mathrm{pSpec} R$ of the prime spectrum of the ring $R$ modulo the equivalence generated by the inclusion. When every prime ideal contains only one minimal prime, for instance if $R$ is arithmetical, $\mathrm{pSpec} R$ is Hausdorff and there is a bijection between this quotient space and the minimal prime spectrum $\mathrm{Min} R$, which is a homeomorphism if and only if $\mathrm{Min} R$ is compact. If $x$ is a closed point of $\mathrm{pSpec} R$, there is a pure ideal $A(x)$ such that $x=V(A(x))$. If $R$ is almost clean, i.e. each element is the sum of a regular element with an idempotent, it is shown that $\mathrm{pSpec} R$ is totally disconnected and, $\forall x\in\mathrm{pSpec} R$, $R/A(x)$ is almost clean; the converse holds if every principal ideal is finitely presented. Some questions posed by Facchini and Faith at the second International Fez Conference on Commutative Ring Theory in 1995, are also investigated. If $R$ is a commutative ring for which the ring $Q(R/A)$ of quotients of $R/A$ is an IF-ring for each proper ideal $A$, it is proved that $R_P$ is a strongly discrete valuation ring for each maximal ideal $P$ and $R/A$ is semicoherent for each proper ideal $A$

Recollements of Module Categories

We establish a correspondence between recollements of abelian categories up to equivalence and certain TTF-triples. For a module category we show, moreover, a correspondence with idempotent ideals, recovering a theorem of Jans. Furthermore, we show that a recollement whose terms are module categories is equivalent to one induced by an idempotent element, thus answering a question by Kuhn.Comment: Comments are welcom

Meaning and Dialogue Coherence: A Proof-theoretic Investigation

This paper presents a novel proof-theoretic account of dialogue coherence. It focuses on an abstract class of cooperative information-oriented dialogues and describes how their structure can be accounted for in terms of a multi-agent hybrid inference system that combines natural deduction with information transfer and observation. We show how certain dialogue structures arise out of the interplay between the inferential roles of logical connectives (i.e., sentence semantics), a rule for transferring information between agents, and a rule for information flow between agents and their environment. The order of explanation is opposite in direction to that adopted in game-theoretic semantics, where sentence semantics (or a notion of valid inference) is derived from winning dialogue strategies. That approach and the current one may, however, be reconcilable, since we focus on cooperative dialogue, whereas the game-theoretic tradition concentrates on adversarial dialogue

Determination of the basin of attraction of a periodic orbit in two dimensions using meshless collocation

A contraction metric for an autonomous ordinary differential equation is a Riemannian metric such that the distance between adjacent solutions contracts over time. A contraction metric can be used to determine the basin of attraction of a periodic orbit without requiring information about its position or stability. Moreover, it is robust to small perturbations of the system. In two-dimensional systems, a contraction metric can be characterised by a scalar-valued function. In [9], the function was constructed as solution of a first-order linear Partial Differential Equation (PDE), and numerically constructed using meshless collocation. However, information about the periodic orbit was required, which needed to be approximated. In this paper, we overcome this requirement by studying a second-order PDE, which does not require any information about the periodic orbit. We show that the second-order PDE has a solution, which defines a contraction metric. We use meshless collocation to approximate the solution and prove error estimates. In particular, we show that the approximation itself is a contraction metric, if the collocation points are dense enough. The method is applied to two examples

Lifting and restricting recollement data

We study the problem of lifting and restricting TTF triples (equivalently, recollement data) for a certain wide type of triangulated categories. This, together with the parametrizations of TTF triples given in "Parametrizing recollement data", allows us to show that many well-known recollements of right bounded derived categories of algebras are restrictions of recollements in the unbounded level, and leads to criteria to detect recollements of general right bounded derived categories. In particular, we give in Theorem 1 necessary and sufficient conditions for a 'right bounded' derived category of a differential graded(=dg) category to be a recollement of 'right bounded' derived categories of dg categories. In Theorem 2 we consider the particular case in which those dg categories are just ordinary algebras.Comment: 29 page

Reproductive Ecology and Severe Pollen Limitation in the Polychromic Tundra Plant, Parrya nudicaulis (Brassicaceae)

Pollen limitation is predicted to be particularly severe in tundra habitats. Numerous reproductive patterns associated with alpine and arctic species, particularly mechanisms associated with reproductive assurance, are suggested to be driven by high levels of pollen limitation. We studied the reproductive ecology of Parrya nudicaulis, a species with relatively large sexual reproductive investment and a wide range of floral pigmentation, in tundra habitats in interior montane Alaska to estimate the degree of pollen limitation. The plants are self-compatible and strongly protandrous, setting almost no seed in the absence of pollinators. Supplemental hand pollinations within pollinator exclusion cages indicated no cage effect on seed production. Floral visitation rates were low in both years of study and particularly infrequent in 2010. A diversity of insects visited P. nudicaulis, though syrphid and muscid flies composed the majority of all visits. Pollen-ovule ratios and levels of heterozygosity are consistent with a mixed mating system. Pollen limitation was severe; hand pollinations increased seed production per plant five-fold. Seed-to-ovule ratios remained low following hand pollinations, indicating resource limitation is likely to also be responsible for curtailing seed set. We suggest that pollen limitation in P. nudicaulis may be the result of selection favoring an overproduction of ovules as a bet-hedging strategy in this environmental context of highly variable pollen receipt