The space missions Voyager and Cassini together with earthbound observations revealed a wealth of structures in Saturn’s rings. There are, for example, waves being excited at ring positions which are in orbital resonance with Saturn’s moons. Other structures can be assigned to embedded moons like empty gaps, moon induced wakes or S-shaped propeller features. Furthermore, irregular radial structures are observed in the range from 10 meters until kilometers. Here some of these structures will be discussed in the frame of hydrodynamical modeling of Saturn’s dense rings. For this purpose we will characterize the physical properties of the ring particle ensemble by mean field quantities and point to the special behavior of the transport coefficients. We show that unperturbed rings can become unstable and how diffusion acts in the rings. Additionally, the alternative streamline formalism is introduced to describe perturbed regions of dense rings with applications to the wake damping and the dispersion relation of the density waves.

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 is devoted to the study of global existence of periodic solutions of a delayedtumor-immune competition model. Also some numerical simulations are given to illustratethe theoretical results

In this paper, we propose a computational model to investigate the coupling between cell’s adhesions and actin fibres and how this coupling affects cell shape and stability. To accomplish that, we take into account the successive stages of adhesion maturation from adhesion precursors to focal complexes and ultimately to focal adhesions, as well as the actin fibres evolution from growing filaments, to bundles and finally contractile stress fibres.

We use substrates with discrete patterns of adhesive patches, whose inter-patches distance can be modulated in order to control the location of the adhesions and the resulting fibres architecture. We then investigate the emergence of stable cell morphologies as a function of the inter-patches distance, for two different cell phenotypes generated from the model. Force generated by the stress fibres on the focal adhesions and specifically the influence of the cell contractility are also investigated.

Our results suggest that adhesion lifetime and fibre growing rate are the key parameters in the emergence of stable cell morphologies and the limiting factors for the magnitude of the mean tension force from the fibres on the focal adhesions.

We present a new method for generating a d-dimensional simplicial meshthat minimizes the L p -norm,p > 0, of the interpolation error or its gradient. The methoduses edge-based error estimates to build a tensor metric. We describe and analyze thebasic steps of our method

Habitat fragmentation is an important area of concern in species conservation. Habitatfragmentation can affect population distributions through reductions in suitable habitat,and through organism responses to different habitat types and the transitions betweenthem. In earlier work, the effect of habitat fragmentation on cyclic populations wasinvestigated in the context of populations that show no behavioural response to theinterface between habitat types. In this paper, we extend the earlier work by addingedge-mediated behaviour to the models. That is, we investigate the dynamics that resultwhen oscillatory predator and prey species also exhibit behavioural responses to habitatinterfaces. Our results show generally that habitat loss decreases the amplitude and theaverage density of the prey and predator populations, but that most of the reponsesobserved in the two models exhibit marked differences. This work highlights the complexityof the interplay between population cycles, habitat fragmentation, and edge-mediatedbehaviour, and the need to study such systems in greater detail.

Hypercyclicity of C0-semigroups is a very unstable property: We give examples toshow that adding arbitrary small constants or a bounded rank one operator to the generator of ahypercyclic semigroup can destroy hypercyclicity. Also the limit of hypercyclic semigroups (evenin operator norm topology) need not be hypercyclic, and a hypercyclic semigroup can be the limitof nonhypercyclic ones. Hypercyclicity is not inherited by the Yosida approximations. Finally, therestriction of a hypercyclic nonnegative semigroup in a Banach lattice to the positive cone may befar from hypercyclic.

When modeling the spread of infectious diseases, it is important to incorporate riskbehavior of individuals in a considered population. Not only risk behavior, but also thenetwork structure created by the relationships among these individuals as well as thedynamical rules that convey the spread of the disease are the key elements in predictingand better understanding the spread. In this work we propose the weighted randomconnection model, where each individual of the population is characterized by twoparameters: its position and risk behavior. A goal is to model the effect that theprobability of transmissions among individuals increases in the individual risk factors,and decays in their Euclidean distance. Moreover, the model incorporates a combined riskbehavior function for every pair of the individuals, through which the spread can bedirectly modeled or controlled. We derive conditions for the existence of an outbreak ofinfectious diseases in this model. Our main result is the almost sure existence of aninfinite component in the weighted random connection model. We use results on the randomconnection model and site percolation in Z2.

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.

The basic reproduction number, R0, is often defined as the averagenumber of infections generated by a newly infected individual in a fully susceptiblepopulation. The interpretation, meaning, and derivation of R0 arecontroversial. However, in the context of mean field models, R0 demarcatesthe epidemic threshold below which the infected population approaches zero in the limit oftime. In this manner, R0 has been proposed as a method forunderstanding the relative impact of public health interventions with respect to diseaseeliminations from a theoretical perspective. The use of R0 is made morecomplex by both the strong dependency of R0 on the model form and the stochasticnature of transmission. A common assumption in models of HIV transmission that have closedform expressions for R0 is that a single individual’sbehavior is constant over time. In this paper we derive expressions for bothR0 and probability of an epidemic in afinite population under the assumption that people periodically change their sexualbehavior over time. We illustrate the use of generating functions as a general frameworkto model the effects of potentially complex assumptions on the number of transmissionsgenerated by a newly infected person in a susceptible population. We find that therelationship between the probability of an epidemic and R0 is notstraightforward, but, that as the rate of change in sexual behavior increases bothR0 and the probability of an epidemic alsodecrease.

How does DNA, the molecule containing genetic information, change its three-dimensionalshape during the complex cellular processes of replication, recombination and repair? Thisis one of the core questions in molecular biology which cannot be answered without helpfrom mathematical modeling. Basic concepts of topology and geometry can be introduced inundergraduate teaching to help students understand counterintuitive complex structuraltransformations that occur in every living cell. Topoisomerases, a fascinating class ofenzymes involved in replication, recombination and repair, catalyze a change in DNAtopology through a series of highly coordinated mechanistic steps. Undergraduate biologyand mathematics students can visualize and explore the principles of topoisomerase actionby using easily available materials such as Velcro, ribbons, telephone cords, zippers andtubing. These simple toys can be used as powerful teaching tools to engage students inhands-on exploration with the goal of learning about both the mathematics and the biologyof DNA structure.

In the present paper, a general multiobjective optimization problem is stated as a Nashgame. In the nonrestrictive case of two objectives, we address the problem of thesplitting of the design variable between the two players. The so-called territorysplitting problem is solved by means of an allocative approach. We propose two algorithmsin order to find fair allocation tables

In this paper we deal with a model describing the evolution in time of the density of aneural population in a state space, where the state is given by Izhikevich’s two -dimensional single neuron model. The main goal is to mathematically describe theoccurrence of a significant phenomenon observed in neurons populations, thesynchronization. To this end, we are making the transition to phasedensity population, and use Malkin theorem to calculate the phase deviations of a weaklycoupled population model.

We consider the stabilization of a rotating temperature pulse traveling in a continuousasymptotic model of many connected chemical reactors organized in a loop with continuouslyswitching the feed point synchronously with the motion of the pulse solution. We use theswitch velocity as control parameter and design it to follow the pulse: the switchvelocity is updated at every step on-line using the discrepancy between the temperature atthe front of the pulse and a set point. The resulting feedback controller, which can beregarded as a dynamic sampled-data controller, is designed using root-locus technique.Convergence conditions of the control law are obtained in terms of the zero structure(finite zeros, infinite zeros) of the related lumped model.

An optimal control problem is studied for a predator-prey system of PDE, with a logisticgrowth rate of the prey and a general functional response of the predator. The controlfunction has two components. The purpose is to maximize a mean density of the two speciesin their habitat. The existence of the optimal solution is analyzed and some necessaryoptimality conditions are established. The form of the optimal control is found in someparticular cases.

The heat equation is considered in the complex system consisting of many small bodies(particles) embedded in a given material. On the surfaces of the small bodies aNewton-type boundary condition is imposed. An equation for the limiting field is derivedwhen the characteristic size a of the small bodies tends to zero, theirtotal number \hbox{$\mathcal{N}(a)$}𝒩(a) tends to infinity at a suitable rate, and the distanced = d(a) between neighboring smallbodies tends to zero a <  < d. No periodicity isassumed about the distribution of the small bodies.

We first investigate linear size-structured population models with spacial diffusion. Existence of a unique mild solution is established. Then we consider a harvesting problem for linear size-structured models with diffusion and show the existence of an optimal harvesting effort to maximize the total price or total harvest.

We study the behavior of linear nonstationary shallow water waves generated by aninstantaneous localized source as they propagate over and become trapped by elongatedunderwater banks or ridges. To find the solutions of the corresponding equations, we usean earlier-developed asymptotic approach based on a generalization of Maslov’s canonicaloperator, which provides a relatively simple and efficient analytic-numerical algorithmfor the wave field computation. An analysis of simple examples (where the bank and sourceshapes are given by certain elementary functions) shows that the appearance and dynamicsof trapped wave trains is closely related to a cascade of bifurcations of space-timecaustics, the bifurcation parameter being the bank length-to-width ratio.

We review some recent results concerning Gibbs measures for nonlinear Schrödingerequations (NLS), with implications for the theory of the NLS, including stability andtypicality of solitary wave structures. In particular, we discuss the Gibbs measures ofthe discrete NLS in three dimensions, where there is a striking phase transition tosoliton-like behavior.

We develop the qualitative theory of thesolutions of the McKendrick partial differential equation ofpopulation dynamics. We calculate explicitly the weak solutionsof the McKendrick equation and of the Lotka renewal integralequation with time and age dependent birth rate. Mortality modulusis considered age dependent. We show the existence of demographycycles. For a population with only one reproductive age class,independently of the stability of the weak solutions and after atransient time, the temporal evolution of the number ofindividuals of a population is always modulated by a time periodicfunction. The periodicity of the cycles is equal to the age ofthe reproductive age class, and a population retains the memoryfrom the initial data through the amplitude of oscillations. For apopulation with a continuous distribution of reproductive ageclasses, the amplitude of oscillation is damped. The periodicityof the damped cycles is associated with the age of the firstreproductive age class. Damping increases as the dispersion of thefertility function around the age class with maximal fertilityincreases. In general, the period of the demography cycles isassociated with the time that a species takes to reach thereproductive maturity.