Stimuli-responsive polymers result inon-demand regulation of properties and functioning of variousnanoscale systems. In particular, they allow stimuli-responsivecontrol of flow rates through membranes and nanofluidic deviceswith submicron channel sizes. They also allow regulation of drugrelease from nanoparticles and nanofibers in response totemperature or pH variation in the surrounding medium. In thepresent work two relevant mathematical models are introduced toaddress precipitation-driven deposition of surface layers ofstimuli-responsive polymers and describe a possible effect ofswelling-shrinkage transition of such polymers on drug release.

We present a brief review of molecular biological basis and mathematical modelling of circadian rhythms in Drosophila. We discuss pertinent aspects of a new modelthat incorporates the transcriptional feedback loops revealed so far in the network of thecircadian clock (PER/TIM and VRI/PDP1 loops). Conventional Hill functions are not usedto describe the regulation of genes, instead the explicit reactions of binding and unbindingprocesses of transcription factors to promoters are probabilistically modelled. The modelis described by a set of ordinary differential equations, and the parameters are estimatedfrom the in vitro experimental data of the clocks' components. The model is robust over awide range of parameter variations. Through the sensitivity analysis of the model, roles ofVRI and PDP1 feedback loops are investigated, and it is proposed that they increase therobustness of the clock.

Intra-specific competition in population dynamics can be described by integro-differentialequations where the integral term corresponds to nonlocal consumption of resources by individualsof the same population. Already the single integro-differential equation can show theemergence of nonhomogeneous in space stationary structures and can be used to model the processof speciation, in particular, the emergence of biological species during evolution [S. Genieys et al., Math. Model. Nat. Phenom. 1 (2006), no. 1, 65-82], [S. Genieys et al., Comptes Rendus Biologies, 329 (11), 876-879 (2006)]. Onthe other hand, competition of two different species represents a well known and well studiedmodel in population dynamics. In this work we study how the intra-specific competition can influencethe competition between species. We will prove the existence of travelling waves for the casewhere the support of the kernel of the integral is sufficiently narrow. Numerical simulations willbe carried out in the case of large supports.

We have explored the combined long-wave Marangoni and Rayleigh instability ofthe quiescent state of a binary- liquid layer heated from below or from above in the presenceof the Soret effect. We found that in the case of small Biot numbers there are two long-wave regions of interest k ~ Bi 1/2 and k ~ Bi 1/4. The dependence of both monotonic andoscillatory thresholds of instability in these regions on both the Soret and dynamic Bondnumbers has been investigated. The complete linear stability analysis reveals the diversityof instability types in the long-wave region, and a need in the development of the nonlineartheory of the discovered phenomena becomes obvious.

This contribution reviews the nonlinearstochastic properties of turbulent velocity and passive scalarintermittent fluctuations in Eulerian and Lagrangian turbulence.These properties are illustrated with original data sets of (i)velocity fluctuations collected in the field and in thelaboratory, and (ii) temperature, salinity and in vivofluorescence (a proxy of phytoplankton biomass, i.e. unicelledvegetals passively advected by turbulence) sampled from highlyturbulent coastal waters. The strength of three of the mostpopular models describing intermittent fluctuations (thelognormal, log-Lévy and log-Poisson models) to fit thedistribution of in vivo fluorescence has subsequently beencritically assessed. A theoretical formulation for the stochasticproperties of biologically active scalars is also provided andvalidated. Finally, the potential effect of the intermittentproperties of turbulent velocity fluctuations on processesrelevant to the life of plankton organisms are theoreticallyinvestigated. It is shown that the intermittent nature ofmicroscale turbulence may result in (i) a decrease in the rate ofnutrient fluxes towards non-motile phytoplankton cells (6-62 %),(ii) a decrease in the physical coagulation of phytoplankton cells(25-48 %) and in the subsequent phytoplankton aggregate volumes(22-41 %), and (iii) a decrease of the turbulence contribution topredator-prey encounter rates (25-50 %).

We compare dewetting characteristics of a thin nonwetting solid film in theabsence of stress, fortwo models of a wetting potential: the exponential and the algebraic.The exponential model is a one-parameter (r) model, and the algebraic model isa two-parameter (r, m)model, where r is the ratio of the characteristic wetting length to the heightof the unperturbed film,and m is the exponent of h (film height) in a smooth function thatinterpolates the system's surfaceenergy above and below the film-substrate interface at z = 0. The exponentialmodelgives monotonically decreasing (with h) wetting chemical potential, whilethis dependence is monotonic only for the m = 1 case of the algebraic model.Linear stability analysis of the planar equilibrium surface is performed.Simulations of the surface dynamics in the strongly nonlinear regime(large deviations from the planar equilibrium) and for large surface energyanisotropies demonstrate that for any m the film is less prone to dewettingwhen it is governed by the algebraic model. Quasiequilibrium states similar tothe one found in the exponential model [M. Khenner, Phys. Rev. B, 77 (2008), 245445.] exist in the algebraic model as well, and the film morphologies are similar.

This paper introduces a new approach for the joint alignment of a largecollection of segmented images into the same system of coordinates whileestimating at the same time an optimal common coordinate system. The atlasresulting from our group-wise alignment algorithm is obtained as the hiddenvariable of an Expectation-Maximization (EM) estimation. This is achievedby identifying the most consistent label across the collection of images at eachvoxel in the common frame of coordinates.
In an iterative process, each subject is iteratively aligned with the currentprobabilistic atlas until convergence of the estimated atlas is reached. Twodifferent transformation models are successively applied in the alignmentprocess: an affine transformation model and a dense non-rigiddeformation field. The metric for both transformation models is the mutualinformation that is computed between the probabilistic atlas and each subject.This metric is optimized in the affine alignment step using a gradient basedstochastic optimization (SPSA) and with a variational approach to estimate thenon-rigid atlas to subject transformations.
A first advantage of our method is that the computational cost increaseslinearly with the number of subjects in the database. This method is thereforeparticularly suited for a large number of subjects. Another advantage is that,when computing the common coordinate system, the estimation algorithm identifiesweights for each subject on the basis of the typicality of the segmentation.This makes the common coordinate system robust to outliers in the population.
Several experiments are presented in this paper to validate our atlasconstruction method on a population of 80 brain images segmented into 4 labels(background, white and gray matters and ventricles). First, the 80 subjects werealigned using affine and dense non-rigid deformation models. The results arevisually assessed by examining how the population converges closer toa central tendency when the deformation model allows more degrees of freedom(from affine to dense non-rigid field). Second, the stability of the atlasconstruction procedure for various sizes of population was investigated bystarting from a subset of the total population which was incrementallyaugmented until the total population of 80 subjects was reached. Third, theconsistency of our group-wise reference (hidden variable of the EM algorithm)was also compared to the choice of an arbitrary subject for a subset of 10subjects. According to William's index, our reference choiceperformed favorably. Finally, the performance of our algorithm was quantified ona synthetic population of 10 subjects (generated using random B-Splinetransformations) using a global overlap measure for each label. We also measuredthe robustness of this measure to the introduction of noisy subjects in thepopulation.

A model of chemotaxis is analyzed that prevents blow-up of solutions. The modelconsists of a system of nonlinear partial differential equations for the spatial populationdensity of a species and the spatial concentration of a chemoattractant in n-dimensionalspace. We prove the existence of solutions, which exist globally, and are L∞-bounded onfinite time intervals. The hypotheses require nonlocal conditions on the species-inducedproduction of the chemoattractant.

A one-dimensional lattice of SIR (susceptible/infected/removed) epidemic centres isconsidered numerically and analytically. The limiting solutions describing the behaviour of thestandard SIR model with a small number of initially infected individuals are derived, and expressionsfound for the duration of an outbreak. We study a model for a weakly mixed populationdistributed between the interacting centres. The centres are modelled as SIR nodes with interactionbetween sites determined by a diffusion-type migration process. Under the assumption of fastmigration, a one-dimensional lattice of SIR nodes is studied numerically with deterministic andrandom coupling, and travelling wave-like solutions are found in both cases. For weak coupling,the main part of the travelling wave is well approximated by the limiting SIR solution. Explicitformulae are found for the speed of the travelling waves and compared with results of numericalsimulation. Approximate formulae for the epidemic propagation speed are also derived whencoupling coefficients are randomly distributed, they allow us to estimate how the average speed inrandom media is slowed down.

The spatio-temporal dynamics of a population present one of the most fascinating aspects and challenges for ecological modelling. In this article we review some simple mathematical models, based on one dimensional reaction-diffusion-advection equations, for the growth of a population on a heterogeneous habitat. Considering a number of models of increasing complexity we investigate the often contrary roles of advection and diffusion for the persistence of the population. When it is possible we demonstrate basic mathematical techniques and give the critical conditions providing the survival of a population in simple systems and in more complex resource-consumer models which describe the dynamics of phytoplankton in a water column.

Marangoni convection caused by a photochemical reaction of the type A $\stackrel{h\nu}{\rightleftharpoons}$ B in a deep liquid layer is studied. Linear stability analysis is performed and the conditionsfor Marangoni convection to occur are obtained. It is shown that increasing the rate of thedirect reaction, for example, by increasing the light intensity, destabilizes the steady stateand causes convective motion of the fluid, whereas increasing the rate of the inverse reactionstabilizes the steady state. A weakly nonlinear analysis of the problem is performed thatgives conditions for hexagonal convective patters to occur. It is shown that, in the case ofsmall light absorption length, the hexagonal cells correspond to "down"-hexagons.

Studying the evolutive and adaptative machanisms of prokayotes is a complicated task.As these machanisms cannot be easily studied "in vivo", it is necessary to consider other methods.We have therefore developed the RAevol model, a model designed to study the evolution of bacteria and their adaptationto the environment.Our model simulates the evolution of a population of artificial bacteria in a changing environment, providing us with an insight into the strategies that digital organisms develop to adapt to new conditions.In this paper we describe the principle and architecture of the model, focusing on the mechanisms of the regulatory networks of artificial organisms.Experiments were conducted on populations of artificial bacteria under conditions of stress.We study the ways in which organisms adapt to environmental changes and examine the strategies they adopt.An analysis of these adaptation strategies is presented and a brief overview was proposed concerning the patterns and topological characteristics of the evolved regulatory networks.

No other concepts have shaken so deeply the bases of engineering like those of positiveand negative feedback. They have played a most prominent role in engineering since the beginningof the previous century. The birth certificate of positive feedback can be traced back to a pair ofpatents by Edwin H. Armstrong in 1914 and 1922, whereas that of negative feedback is alreadylost in time. We present in this paper a short review on the feedback's origins in the fields ofengineering and biology. Besides, we compare the main feedback's ideas in control theory andsystem biology in order to get a better understanding of the lactose and tryptophan operons' regulatorysystems (control systems). It is obvious that we need to know the genome of an organismin order to understand how it works, but that is only half of the puzzle, for we also need to knowhow the underlying genetic regulatory systems work in order to get a complete picture of the cell'sdynamics.

Basic models suitable to explain the epidemiology of dengue fever have previouslyshown the possibility of deterministically chaotic attractors, which might explain the observedfluctuations found in empiric outbreak data. However, the region of bifurcations and chaos requirestrong enhanced infectivity on secondary infection, motivated by experimental findings ofantibody-dependent-enhancement. Including temporary cross-immunity in such models, which iscommon knowledge among field researchers in dengue, we find bifurcations up to chaotic attractorsin much wider and also unexpected parameter regions of reduced infectivity on secondaryinfection, realistically describing more likely hospitalization on secondary infection when the viralload becomes high. The model shows Hopf bifurcations, symmetry breaking bifurcations of limitcycles, coexisting isolas, and two different possible routes to chaos, via the Feigenbaum perioddoubling and via torus bifurcations.

We consider the formation of solid drops(“islands”) occurring in the growth of strained solidfilms. Beginning from a detailed model for the growth of an alloy filmthat incorporates the coupling between composition, elastic stress andthe morphology of the free boundary, we develop an asymptoticdescription of the shape and compositional nonuniformity of smallalloy islands grown at small deposition rates. A key feature of theanalysis is a “thin domain” scaling in the island which enablesrecasting the free boundary problem into a set of integrodifferentialequations for the shape and composition profile. Theintegrodifferential system can be decomposed into two parts: one partgives a single integrodifferential equation for the shape analogous tothat obtained for a single-component island determined by Shanahan andSpencer (2002), and the other part gives the composition profile interms of the shape. Thus, the shape of an alloy island is identical tothat of a single-component island with the same system parameters, butwith a nonuniform composition that depends on the stress-compositioncoupling and alloy solution thermodynamics. Finally, we characterizethe structure and magnitude of the compositional nonuniformity andalso interpret our theoretical results in the context of SiGe alloyfilms.

This paper is devoted to the study of a predator-prey model in a patchy environment.The model represents the interactions between phytoplankton and zooplankton in the water column.Two patches are considered with respect to light availability: one patch is associated to thesurface layer, the second patch describes the bottom layer. We show that this spatial heterogeneitymay destabilize the predator-prey system, even in oligotrophic system where the nutrient is lowenough to avoid ”paradox-enrichment” phenomenon. Indeed, in this case, an heterogeneity indexcan be used as a bifurcation parameter, leading to a Hopf bifurcation. Moreover, we assume that individualscan be dispersed in both patches via hydrodynamism processes, like in a mixed layer. Theeffect of mixing intensity is analysed as well as interactions between dispersion and enrichment.We also show that, in some cases, spatial heterogeneity has a stabilizing effect. These contrastedresults are examined by considering the non linear interaction between heterogeneity, dispersal andenrichment and some mechanisms leading to stabilization/destabilization are exhibited.

We present formulas for the growth rate of surface displacements in phase changeproblems and flow problems in cylindrical geometries under equilibrium conditions. Our goalis to learn when domain dynamics is important vis-a-vis surface dynamics.

Multifractal analysis is known as a useful tool in signal analysis. However, themethods are often used without methodological validation. In this study, wepresent multidimensional models in order to validate multifractal analysismethods.