New delay-dependent stability criteria for uncertain neutral systems with mixed time-varying delays and nonlinear perturbations

The problem of stability analysis for a class of neutral systems with mixed time-varying neutral, discrete and distributed delays and nonlinear parameter perturbations is addressed. By introducing a novel Lyapunov-Krasovskii functional and combining the descriptor model transformation, the Leibniz-Newton formula, some free-weighting matrices, and a suitable change of variables, new sufficient conditions are established for the stability of the considered system, which are neutral-delay-dependent, discrete-delay-range dependent, and distributeddelay-dependent. The conditions are presented in terms of linear matrix inequalities (LMIs) and can be efficiently solved using convex programming techniques. Two numerical examples are given to illustrate the efficiency of the proposed method

EU's democracy promotion policy in the Mediterranean: Squaring the stability – democracy circle?

Why does the EU have an ambiguous and inconsistent democracy promotion (DP) policy towards the Mediterranean countries? This paper argues that the EU´s DP is determined by a crucial conflict of interests conceptualised as a stability – democracy dilemma. The EU has been attempting to promote democracy, but without risking the current stability and in connivance with incumbent autocratic regimes. In view of this dilemma, the four main characteristics of the EU´s DP promotion are explored, namely: gradualism, a strong notion of partnership-building, a narrow definition of civil society, and a strong belief in economic liberalisation. A fifth feature, relation of the EU with moderate Islamists, is analysed in the paper as it represents the most striking illustration of its contradictions. The paper concludes by arguing that the definition of a clear DP by the EU that considered engagement with moderate Islamists would represent a major step towards squaring its stability – democracy circle.

Normal forms, stability and splitting of invariant manifolds I. Gevrey Hamiltonians

In this paper, we give a new construction of resonant normal forms with a small remainder for near-integrable Hamiltonians at a quasi-periodic frequency. The construction is based on the special case of a periodic frequency, a Diophantine result concerning the approximation of a vector by independent periodic vectors and a technique of composition of periodic averaging. It enables us to deal with non-analytic Hamiltonians, and in this first part we will focus on Gevrey Hamiltonians and derive normal forms with an exponentially small remainder. This extends a result which was known for analytic Hamiltonians, and only in the periodic case for Gevrey Hamiltonians. As applications, we obtain an exponentially large upper bound on the stability time for the evolution of the action variables and an exponentially small upper bound on the splitting of invariant manifolds for hyperbolic tori, generalizing corresponding results for analytic Hamiltonians.

Normal forms, stability and splitting of invariant manifolds II. Finitely differentiable Hamiltonians

This paper is a sequel to ``Normal forms, stability and splitting of invariant manifolds I. Gevrey Hamiltonians", in which we gave a new construction of resonant normal forms with an exponentially small remainder for near-integrable Gevrey Hamiltonians at a quasi-periodic frequency, using a method of periodic approximations. In this second part we focus on finitely differentiable Hamiltonians, and we derive normal forms with a polynomially small remainder. As applications, we obtain a polynomially large upper bound on the stability time for the evolution of the action variables and a polynomially small upper bound on the splitting of invariant manifolds for hyperbolic tori.

Preference, specificity and cheating in the arbuscular mycorrhizal symbiosis.

Arbuscular mycorrhizal symbioses are mutualistic interactions between fungi and most plants. There is considerable interest in this symbiosis because of the strong nutritional benefits conferred to plants and its influence on plant diversity. Until recently, the symbiosis was assumed to be unspecific. However, two studies have now revealed that although it can be largely unspecific with the fungal community composition changing seasonally, in certain ecosystems it can also be highly specific and might potentially allow plants to cheat the arbuscular mycorrhizal network that connects plants below ground.

Stochastic stability and the evolution of coordination in spatially structured populations.

Animals can often coordinate their actions to achieve mutually beneficial outcomes. However, this can result in a social dilemma when uncertainty about the behavior of partners creates multiple fitness peaks. Strategies that minimize risk ("risk dominant") instead of maximizing reward ("payoff dominant") are favored in economic models when individuals learn behaviors that increase their payoffs. Specifically, such strategies are shown to be "stochastically stable" (a refinement of evolutionary stability). Here, we extend the notion of stochastic stability to biological models of continuous phenotypes at a mutation-selection-drift balance. This allows us to make a unique prediction for long-term evolution in games with multiple equilibria. We show how genetic relatedness due to limited dispersal and scaled to account for local competition can crucially affect the stochastically-stable outcome of coordination games. We find that positive relatedness (weak local competition) increases the chance the payoff dominant strategy is stochastically stable, even when it is not risk dominant. Conversely, negative relatedness (strong local competition) increases the chance that strategies evolve that are neither payoff nor risk dominant. Extending our results to large multiplayer coordination games we find that negative relatedness can create competition so extreme that the game effectively changes to a hawk-dove game and a stochastically stable polymorphism between the alternative strategies evolves. These results demonstrate the usefulness of stochastic stability in characterizing long-term evolution of continuous phenotypes: the outcomes of multiplayer games can be reduced to the generic equilibria of two-player games and the effect of spatial structure can be analyzed readily.

A repeated GGA motif is critical for the activity and stability of the riboregulator RsmY of Pseudomonas fluorescens.

The riboregulator RsmY of Pseudomonas fluorescens strain CHA0 is an example of small regulatory RNAs belonging to the global Rsm/Csr regulatory systems controlling diverse cellular processes such as glycogen accumulation, motility, or formation of extracellular products in various bacteria. By binding multiple molecules of the small regulatory protein RsmA, RsmY relieves the negative effect of RsmA on the translation of several target genes involved in the biocontrol properties of strain CHA0. RsmY and functionally related riboregulators have repeated GGA motifs predicted to be exposed in single-stranded regions, notably in the loops of hairpins. The secondary structure of RsmY was corroborated by in vivo cleavage with lead acetate. RsmY mutants lacking three or five (out of six) of the GGA motifs showed reduced ability to derepress the expression of target genes in vivo and failed to bind the RsmA protein efficiently in vitro. The absence of GGA motifs in RsmY mutants resulted in reduced abundance of these transcripts and in a shorter half-life (< or = 6 min as compared with 27 min for wild type RsmY). These results suggest that both the interaction of RsmY with RsmA and the stability of RsmY strongly depend on the GGA repeats and that the ability of RsmY to interact with small regulatory proteins such as RsmA may protect this RNA from degradation.

Simulation methods with extended stability for stiff biochemical kinetics

Background: With increasing computer power, simulating the dynamics of complex systems in chemistry and biology is becoming increasingly routine. The modelling of individual reactions in (bio)chemical systems involves a large number of random events that can be simulated by the stochastic simulation algorithm (SSA). The key quantity is the step size, or waiting time, τ, whose value inversely depends on the size of the propensities of the different channel reactions and which needs to be re-evaluated after every firing event. Such a discrete event simulation may be extremely expensive, in particular for stiff systems where τ can be very short due to the fast kinetics of some of the channel reactions. Several alternative methods have been put forward to increase the integration step size. The so-called τ-leap approach takes a larger step size by allowing all the reactions to fire, from a Poisson or Binomial distribution, within that step. Although the expected value for the different species in the reactive system is maintained with respect to more precise methods, the variance at steady state can suffer from large errors as τ grows. Results: In this paper we extend Poisson τ-leap methods to a general class of Runge-Kutta (RK) τ-leap methods. We show that with the proper selection of the coefficients, the variance of the extended τ-leap can be well-behaved, leading to significantly larger step sizes.Conclusions: The benefit of adapting the extended method to the use of RK frameworks is clear in terms of speed of calculation, as the number of evaluations of the Poisson distribution is still one set per time step, as in the original τ-leap method. The approach paves the way to explore new multiscale methods to simulate (bio)chemical systems.

The control of microtubule stability in vitro and in transfected cells by MAP1B and SCG10.

In neurons, the regulation of microtubules plays an important role for neurite outgrowth, axonal elongation, and growth cone steering. SCG10 family proteins are the only known neuronal proteins that have a strong destabilizing effect, are highly enriched in growth cones and are thought to play an important role during axonal elongation. MAP1B, a microtubule-stabilizing protein, is found in growth cones as well, therefore it was important to test their effect on microtubules in the presence of both proteins. We used recombinant proteins in microtubule assembly assays and in transfected COS-7 cells to analyze their combined effects in vitro and in living cells, respectively. Individually, both proteins showed their expected activities in microtubule stabilization and destruction respectively. In MAP1B/SCG10 double-transfected cells, MAP1B could not protect microtubules from SCG10-induced disassembly in most cells, in particular not in cells that contained high levels of SCG10. This suggests that SCG10 is more potent to destabilize microtubules than MAP1B to rescue them. In microtubule assembly assays, MAP1B promoted microtubule formation at a ratio of 1 MAP1B per 70 tubulin dimers while a ratio of 1 SCG10 per two tubulin dimers was needed to destroy microtubules. In addition to its known binding to tubulin dimers, SCG10 binds also to purified microtubules in growth cones of dorsal root ganglion neurons in culture. In conclusion, neuronal microtubules are regulated by antagonistic effects of MAP1B and SCG10 and a fine tuning of the balance of these proteins may be critical for the regulation of microtubule dynamics in growth cones.

Review of Stability Berm Alternatives for Environmentally Senstitive Areas, 2005

Stability berms are commonly constructed where roadway embankments cross soft or unstable ground conditions. Under certain circumstances, the construction of stability berms cause unfavorable environmental impacts, either directly or indirectly, through their effect on wetlands, endangered species habitat, stream channelization, longer culvert lengths, larger right-of-way purchases, and construction access limits. Due to an ever more restrictive regulatory environment, these impacts are problematic. The result is the loss of valuable natural resources to the public, lengthy permitting review processes for the department of transportation and permitting agencies, and the additional expenditures of time and money for all parties. The purpose of this project was to review existing stability berm alternatives for potential use in environmentally sensitive areas. The project also evaluates how stabilization technologies are made feasible, desirable, and cost-effective for transportation projects and determines which alternatives afford practical solutions for avoiding and minimizing impacts to environmentally sensitive areas. An online survey of engineers at state departments of transportation was also conducted to assess the frequency and cost effectiveness of the various stabilization technologies. Geotechnical engineers that responded to the survey overwhelmingly use geosynthetic reinforcement as a suitable and cost-effective solution for stabilizing embankments and cut slopes. Alternatively, chemical stabilization and installation of lime/cement columns is rarely a remediation measure employed by state departments of transportation.

Effect of mating history on gender preference in the hermaphroditic snail physa acuta

Several internally fertilizing hermaphroditic animals can only perform one sexual role at a time. In such species, two individuals that engage in a copulation may have different interests in acting as male or female. A gender choice must be made which, if both individuals have the same preference, may give rise to a severe sexual conflict. Here we tested the hypothesis that gender choice could be influenced by mating history, using the freshwater snail, Physa acuta. We recorded the copulatory behaviour of 240 pairs composed of a focal individual and a partner, each either short- or long-isolated. We found that the time to the first copulation was unaffected by isolation status, suggesting that first contacts in this species are random processes. In contrast, the duration of copulations and the frequency of rejection behaviours suggested that individual gender preference switches from male biased to female biased as isolation increases. In addition, snails rejected copulations more frequently when presented to a partner with the same isolation status. Reciprocity, measured as the rate of gender swapping between the first and second copulations, was high irrespective of gender status. We suggest possible evolutionary causes for this gender preference switch and discuss its potential importance in natural population as well as its consequences for the maintenance of hermaphroditism

Non-Quasi-Competitiveness and Stability in Cournot's Model

This paper retakes previous work of the authors, about the relationship between non-quasi-competitiveness (the increase in price caused by an increase in the number of oligopolists) and stability of the equilibrium in the classical Cournot oligopoly model. Though it has been widely accepted in the literature that the loss of quasi-competitiveness is linked, in the long run as new firms entered the market, to instability of the model, the authors in their previous work put forward a model in which a situation of monopoly changed to duopoly losing quasi-competitiveness but maintaining the stability of the equilibrium. That model could not, at the time, be extended to any number of oligopolists. The present paper exhibits such an extension. An oligopoly model is shown in which the loss of quasi-competitiveness resists the presence in the market of as many firms as one wishes and where the successive Cournot's equilibrium points are unique and asymptotically stable. In this way, for the first time, the conjecture that non-quasi- competitiveness and instability were equivalent in the long run, is proved false.