Nullity conditions in paracontact geometry

The paper is a complete study of paracontact metric manifolds for which the Reeb vector field of the underlying contact structure satisfies a nullity condition (the condition \eqref{paranullity} below, for some real numbers $\tilde\kappa$ and $\tilde\mu$). This class of pseudo-Riemannian manifolds, which includes para-Sasakian manifolds, was recently defined in \cite{MOTE}. In this paper we show in fact that there is a kind of duality between those manifolds and contact metric $(\kappa,\mu)$-spaces. In particular, we prove that, under some natural assumption, any such paracontact metric manifold admits a compatible contact metric $(\kappa,\mu)$-structure (eventually Sasakian). Moreover, we prove that the nullity condition is invariant under $\mathcal{D}$-homothetic deformations and determines the whole curvature tensor field completely. Finally non-trivial examples in any dimension are presented and the many differences with the contact metric case, due to the non-positive definiteness of the metric, are discussed.Comment: Different. Geom. Appl. (to appear

Uniform approximation of solutions by elimination of intermediate species in deterministic reaction networks

Chemical reactions often proceed through the formation and the consumption of intermediate species. An example is the creation and subsequent degradation of the substrate-enzyme complexes in an enzymatic reaction. In this paper we provide a setting, based on ordinary differential equations, in which the presence of intermediate species has little effect on the overall dynamics of a biological system. The result provides a method to perform model reduction by elimination of intermediate species. We study the problem in a multiscale setting, where the species abundances as well as the reaction rates scale to different orders of magnitudes. The different time and concentration scales are parameterized by a single parameter N. We show that a solution to the original reaction system is uniformly approximated on compact time intervals to a solution of a reduced reaction system without intermediates and to a solution of a certain limiting reaction systems, which does not depend on N. Known approximation techniques such as the theorems by Tikhonov and Fenichel cannot readily be used in this framework

Elimination of intermediate species in multiscale stochastic reaction networks

We study networks of biochemical reactions modelled by continuous time Markov processes. Such networks typically contain many molecular species and reactions and are hard to study analytically as well as by simulation. Particularly, we are interested in reaction networks with intermediate species such as the substrate-enzyme complex in the Michaelis-Menten mechanism. Such species are virtually in all real-world networks, they are typically short-lived, degraded at a fast rate and hard to observe experimentally. We provide conditions under which the Markov process of a multiscale reaction network with intermediate species is approximated by the Markov process of a simpler reduced reaction network without intermediate species. We do so by embedding the Markov processes into a one-parameter family of processes, where reaction rates and species abundances are scaled in the parameter. Further, we show that there are close links between these stochastic models and deterministic ODE models of the same networks

Product-form poisson-like distributions and complex balanced reaction systems

Stochastic reaction networks are dynamical models of biochemical reaction systems and form a particular class of continuous-time Markov chains on Nn. Here we provide a fundamental characterization that connects structural properties of a network to its dynamical features. Specifically, we define the notion of "stochastically complex balanced systems" in terms of the network's stationary distribution and provide a characterization of stochastically complex balanced systems, parallel to that established in the 1970s and 1980s for deterministic reaction networks. Additionally, we establish that a network is stochastically complex balanced if and only if an associated deterministic network is complex balanced (in the deterministic sense), thereby proving a strong link between the theory of stochastic and deterministic networks. Further, we prove a stochastic version of the "deficiency zero theorem" and show that any (not only complex balanced) deficiency zero reaction network has a product-form Poisson-like stationary distribution on all irreducible components. Finally, we provide sufficient conditions for when a product-form Poisson-like distribution on a single (or all) component(s) implies the network is complex balanced, and we explore the possibility to characterize complex balanced systems in terms of product-form Poisson-like stationary distributions

My Girl Friday

My Girl Friday is an exploration of 1940s/WWII inspired street wear that draws parallels between the tailoring and craftsmanship found in vintage looks, and the relaxed clothing of today

World Wore II

World Wore II is a combination of street wear pieces drawn from the parallels of 1940’s/WWII era seaming and colors, vintage craftsmanship, and modern-day women’s wear. By producing garments using inspiration from old to inspire new, technology becomes a successful tool of creating marketable new craft

Small launch platforms for micro-satellites

The number of small satellites launched into orbit has enormously increased in the last twenty years. The introduction of new standards of micro-satellites has multiplied the launch demand around the world. Nevertheless, not all the missions can easily have access to space: not all kinds of micro-satellites have granted a deployer system and, furthermore, once a micro-satellite is able to reach it, it cannot usually choose its final orbit. Recently two new platforms have been introduced for the release of micro-satellites as piggy-backs. These platforms are totally operative spacecrafts that act like motherships, and allow to select some parameters of the final orbit of the piggy-backs. They provide a solution for three different nano-satellites standard, and at the same time they are being developed in order to reach more powerful orbital release capabilities in the future. The design and the mission of these platforms are described in this paper

Addition of flow reactions preserving multistationarity and bistability

We consider the question whether a chemical reaction network preserves the number and stability of its positive steady states upon inclusion of inflow and outflow reactions. Often a model of a reaction network is presented without inflows and outflows, while in fact some of the species might be degraded or leaked to the environment, or be synthesized or transported into the system. We provide a sufficient and easy-to-check criterion based on the stoichiometry of the reaction network alone and discuss examples from systems biology