A Selection Criterion for Patterns in Reaction-Diffusion Systems

Alan Turing's work in Morphogenesis has received wide attention during the past 60 years. The central idea behind his theory is that two chemically interacting diffusible substances are able to generate stable spatial patterns, provided certain conditions are met. Turing's proposal has already been confirmed as a pattern formation mechanism in several chemical and biological systems and, due to their wide applicability, there is a great deal of interest in deciphering how to generate specific patterns under controlled conditions. However, techniques allowing one to predict what kind of spatial structure will emerge from Turing systems, as well as generalized reaction-diffusion systems, remain unknown. Here, we consider a generalized reaction diffusion system on a planar domain and provide an analytic criterion to determine whether spots or stripes will be formed. It is motivated by the existence of an associated energy function that allows bringing in the intuition provided by phase transitions phenomena. This criterion is proved rigorously in some situations, generalizing well known results for the scalar equation where the pattern selection process can be understood in terms of a potential. In more complex settings it is investigated numerically. Our criterion can be applied to efficiently design Biotechnology and Developmental Biology experiments, or simplify the analysis of hypothesized morphogenetic models.Comment: 19 pages, 10 figure

The New World species of Ataenius Harold, 1867 : 5. Revision of the A. strigatus group (Scarabaeidae: Aphodiinae: Eupariini)

The strigatus group of the New World species of Ataenius Harold is revised. Seventeen species are recognized including two species described as new: Ataenius ecruensis sp. nov. from the United States and A. oaxacaensis sp. nov. from Mexico. Fifteen previously used names are considered valid, three new synonyms are proposed: A. liogaster Bates (= A. edwardsi Chapin syn. nov. = A. hoguei Cartwright and Spangler syn. nov.), A. wenzelii Horn (= A. rudellus Fall, syn. nov.). New state records are presented for A. spretulus (Haldeman) (Washington) and A. cognatus (LeConte) (Indiana, Missouri, and Mississippi). The taxa are diagnosed, keyed and illustrated; available biological information and distribution data are given

The Long and Viscous Road: Uncovering Nuclear Diffusion Barriers in Closed Mitosis

During Saccharomyces cerevisiae closed mitosis, parental identity is sustained by the asymmetric segregation of ageing factors. Such asymmetry has been hypothesized to occur via diffusion barriers, constraining protein lateral exchange in cellular membranes. Diffusion barriers have been extensively studied in the plasma membrane, but their identity and organization within the nucleus remain unknown. Here, we propose how sphingolipid domains, protein rings, and morphological changes of the nucleus may coordinate to restrict protein exchange between nuclear lobes. Our spatial stochastic model is based on several lines of experimental evidence and predicts that, while a sphingolipid domain and a protein ring could constitute the barrier during early anaphase; a sphingolipid domain spanning the bridge between lobes during late anaphase would be entirely sufficient. Additionally, we explore the structural organization of plausible diffusion barriers. Our work shows how nuclear diffusion barriers in closed mitosis may be emergent properties of simple nanoscale biophysical interactions.Comment: 21 pages, 6 figures and supplementary material (including 8 additional figures and a Table

Order Reduction of the Chemical Master Equation via Balanced Realisation

We consider a Markov process in continuous time with a finite number of discrete states. The time-dependent probabilities of being in any state of the Markov chain are governed by a set of ordinary differential equations, whose dimension might be large even for trivial systems. Here, we derive a reduced ODE set that accurately approximates the probabilities of subspaces of interest with a known error bound. Our methodology is based on model reduction by balanced truncation and can be considerably more computationally efficient than the Finite State Projection Algorithm (FSP) when used for obtaining transient responses. We show the applicability of our method by analysing stochastic chemical reactions. First, we obtain a reduced order model for the infinitesimal generator of a Markov chain that models a reversible, monomolecular reaction. In such an example, we obtain an approximation of the output of a model with 301 states by a reduced model with 10 states. Later, we obtain a reduced order model for a catalytic conversion of substrate to a product; and compare its dynamics with a stochastic Michaelis-Menten representation. For this example, we highlight the savings on the computational load obtained by means of the reduced-order model. Finally, we revisit the substrate catalytic conversion by obtaining a lower-order model that approximates the probability of having predefined ranges of product molecules.Comment: 12 pages, 6 figure

Dilution effects in Ho2−x_{2-x}Yx_xSn2_2O7_7: from the Spin Ice to the single-ion magnet

A study of the modifications of the magnetic properties of Ho$_{2-x}$Y$_x$Sn$_2$O$_7$ upon varying the concentration of diamagnetic Y$^{3+}$ ions is presented. Magnetization and specific heat measurements show that the Spin Ice ground-state is only weakly affected by doping for $x\leq 0.3$, even if non-negligible changes in the crystal field at Ho$^{3+}$ occur. In this low doping range $\mu$SR relaxation measurements evidence a modification in the low-temperature dynamics with respect to the one observed in the pure Spin Ice. For $x\to 2$, or at high temperature, the dynamics involve fluctuations among Ho$^{3+}$ crystal field levels which give rise to a characteristic peak in $^{119}$Sn nuclear spin-lattice relaxation rate. In this doping limit also the changes in Ho$^{3+}$ magnetic moment suggest a variation of the crystal field parameters.Comment: 4 pages, 5 figures, proceedings of HFM2008 Conferenc

On the Taylor expansion of probabilistic \u3bb-terms

We generalise Ehrhard and Regnier\u2019s Taylor expansion from pure to probabilistic \u3bb-terms. We prove that the Taylor expansion is adequate when seen as a way to give semantics to probabilistic \u3bb-terms, and that there is a precise correspondence with probabilistic B\uf6hm trees, as introduced by the second author. We prove this adequacy through notions of probabilistic resource terms and explicit Taylor expansion

Doping-induced quantum cross-over in Er2_2Ti2−x_{2-x}Snx_xO7_7

We present the results of the investigation of magnetic properties of the Er$_2$Ti$_{2-x}$Sn$_x$O$_7$ series. For small doping values the ordering temperature decreases linearly with $x$ while the moment configuration remains the same as in the $x = 0$ parent compound. Around $x = 1.7$ doping level we observe a change in the behavior, where the ordering temperature starts to increase and new magnetic Bragg peaks appear. For the first time we present evidence of a long-range order (LRO) in Er$_2$Sn$_2$O$_7$ ($x = 2.0$) below $T_N = 130$ mK. It is revealed that the moment configuration corresponds to a Palmer-Chalker type with a value of the magnetic moment significantly renormalized compared to $x = 0$. We discuss our results in the framework of a possible quantum phase transition occurring close to $x = 1.7$.Comment: accepted in PRB Rapi