We classify the hulls of different limit-periodic potentials and show that the hull of alimit-periodic potential is a procyclic group. We describe how limit-periodic potentialscan be generated from a procyclic group and answer arising questions. As an expositorypaper, we discuss the connection between limit-periodic potentials and profinite groups ascompletely as possible and review some recent results on Schrödinger operators obtained inthis context.

We consider the problem of frictional contact between an piezoelectric body and aconductive foundation. The electro-elastic constitutive law is assumed to be nonlinear andthe contact is modelled with the Signorini condition, nonlocal Coulomb friction law and aregularized electrical conductivity condition. The existence of a unique weak solution ofthe model is established. The finite elements approximation for the problem is presented,and error estimates on the solutions are derived

In order to study the impact of fishing on a grouper population, we propose in this paperto model the dynamics of a grouper population in a fishing territory by using structuredmodels. For that purpose, we have integrated the natural population growth, the fishing,the competition for shelter and the dispersion. The dispersion was considered as aconsequence of the competition. First we prove, that the grouper stocks may be lesssensitive to the removal of large male individuals if female population are totallyprotected. Second, we show that fishing does not disturb the demographic structure of thepopulation. Finally, we prove that female selective fisheries have the potential ofdrastically reduce reproductive rates. We also prove that male fishing decreasescompetition and then increases the total population number.

The goal of this paper is to apply the Continuous Hopfield Networks (CHN) to thePlacement of Electronic Circuit Problem (PECP). This assignment problem has been expressedas Quadratic Knapsack Problem (QKP). To solve the PECP via the CHN, we choose an energyfunction which ensures an appropriate balance between minimization of the cost functionand simultaneous satisfaction of the PECP constraints. In addition, the parameters of thisfunction must avoid some bad local minima. Finally, some computational experiments solvingthe PECP are included

Natural immunity to breast and prostate cancers is predicted by a novel, saturatedordered mutation model fitted to USA (SEER) incidence data, a prediction consistent withthe latest ideas in immunosurveillance. For example, the prevalence of natural immunity tobreast cancer in the white female risk population is predicted to be 76.5%; this immunitymay be genetic and, therefore, inherited. The modeling also predicts that 6.9% of WhiteFemales are born with a mutation necessary to cause breast cancer (the hereditaryform) and, therefore, are at the highest risk of developing it. By contrast,16.6% of White Females are born without any such mutation but are nonetheless susceptibleto developing breast cancer (the sporadic form). The modeling determinesthe required number of ordered mutations for a cell to become cancerous as well as themean time between consecutive mutations for both the sporadic and hereditary forms of thedisease. The mean time between consecutive breast cancer mutations was found to varybetween 2.59 - 2.97 years, suggesting that such mutations are rare events and establishingan upper bound on the lifetime of a breast cell. The prevalence of immunity to breastcancer is predicted to be 79.7% in Blacks, 86.5% in Asians, and 85.8% in Indians.Similarly, the prevalence of immunity to prostate cancer is predicted to be 67.4% forWhites, 50.5% for Blacks, 77.7% for Asians, and 78.6% for Indians. It is of paramountimportance to delineate the mechanism underlying immunity to these cancers.

Evolution of cell populations can be described with dissipative particle dynamics, whereeach cell moves according to the balance of forces acting on it, or with partialdifferential equations, where cell population is considered as a continuous medium. Wecompare these two approaches for some model examples

In this paper, we look at a model depicting the relationship of cancer cells in differentdevelopment stages with immune cells and a cell cycle specific chemotherapy drug. Themodel includes a constant delay in the mitotic phase. By applying optimal control theory,we seek to minimize the cost associated with the chemotherapy drug and to minimize thenumber of tumor cells. Global existence of a solution has been shown for this model andexistence of an optimal control has also been proven. Optimality conditions andcharacterization of the control are discussed.

Hematologic disorders such as the myelodysplastic syndromes (MDS) are discussed. Thelingering controversies related to various diseases are highlighted. A simplebiomathematical model of bone marrow - peripheral blood dynamics in the normal state isproposed and used to investigate cell behavior in normal hematopoiesis from a mathematicalviewpoint. Analysis of the steady state and properties of the model are used to makepostulations about the phenomenon of massive apoptosis in MDS. Simulations of the modelshow situations in which homeostatic equilibrium can be achieved and maintained.Consequently, it is postulated that hematopoietic growth factors may possess thecapabilities of preventing oscillatory dynamics and enhancing faster evolution towardshomeostatic equilibrium.

In proteomics study, Imaging Mass Spectrometry (IMS) is an emerging and very promisingnew technique for protein analysis from intact biological tissues. Though it has showngreat potential and is very promising for rapid mapping of protein localization and thedetection of sizeable differences in protein expression, challenges remain in dataprocessing due to the difficulty of high dimensionality and the fact that the number ofinput variables in prediction model is significantly larger than the number ofobservations. To obtain a complete overview of IMS data and find trace features based onboth spectral and spatial patterns, one faces a global optimization problem. In thispaper, we propose a weighted elastic net (WEN) model based on IMS data processing needs ofusing both the spectral and spatial information for biomarker selection andclassification. Properties including variable selection accuracy of the WEN model arediscussed. Experimental IMS data analysis results show that such a model not only reducesthe number of side features but also helps new biomarkers discovery.

Two main approaches have been considered for modelling the dynamics of the SIS model oncomplex metapopulations, i.e, networks of populations connected by migratory flows whoseconfigurations are described in terms of the connectivity distribution of nodes (patches)and the conditional probabilities of connections among classes of nodes sharing the samedegree. In the first approach migration and transmission/recovery process alternatesequentially, and, in the second one, both processes occur simultaneously. Here we followthe second approach and give a necessary and sufficient condition for the instability ofthe disease-free equilibrium in generic networks under the assumption of limited (orfrequency-dependent) transmission. Moreover, for uncorrelated networks and under theassumption of non-limited (or density-dependent) transmission, we give a bounding intervalfor the dominant eigenvalue of the Jacobian matrix of the model equations around thedisease-free equilibrium. Finally, for this latter case, we study numerically theprevalence of the infection across the metapopulation as a function of the patchconnectivity.

In this paper we have considered a nonlinear and nonautonomous stage-structured HIV/AIDSepidemic model with an imperfect HIV vaccine, varying total population size anddistributed time delay to become infectious due to intracellular delay between initialinfection of a cell by HIV and the release of new virions. Here, we have established somesufficient conditions on the permanence and extinction of the disease by using inequalityanalytical technique. We have obtained the explicit formula of the eventual lower boundsof infected persons. We have introduced some new threshold valuesR 0 and R ∗ and further obtainedthat the disease will be permanent when R 0 > 1 and thedisease will be going to extinct when R ∗ < 1. ByLyapunov functional method, we have also obtained some sufficient conditions for globalasymptotic stability of this model. The aim of the analysis of this model is to trace theparameters of interest for further study, with a view to informing and assistingpolicy-maker in targeting prevention and treatment resources for maximumeffectiveness.

In this note, I wish to describe the first order semiclassical approximation to thespectrum of one frequency quasi-periodic operators. In the case of a sampling functionwith two critical points, the spectrum exhibits two gaps in the leading orderapproximation. Furthermore, I will give an example of a two frequency quasi-periodicoperator, which has no gaps in the leading order of the semiclassical approximation.

Computational models for human decision making are typically based on the properties of bistable dynamical systems where each attractor represents a different decision. A limitation of these models is that they do not readily account for the fragilities of human decision making, such as “choking under pressure”, indecisiveness and the role of past experiences on current decision making. Here we examine the dynamics of a model of two interacting neural populations with mutual time–delayed inhibition. When the input to each population is sufficiently high, there is bistability and the dynamics is determined by the relationship of the initial function to the separatrix (the stable manifold of a saddle point) that separates the basins of attraction of two co–existing attractors. The consequences for decision making include long periods of indecisiveness in which trajectories are confined in the neighborhood of the separatrix and wrong decision making, particularly when the effects of past history and irrelevant information (“noise”) are included. Since the effects of delay, past history and noise on bistable dynamical systems are generic, we anticipate that similar phenomena will arise in the setting of other physical, chemical and neural time–delayed systems which exhibit bistability.

In this work, we present some concepts recently introduced in the analysis and control ofdistributed parameter systems: Spreadability,vulnerability and protector control. These conceptspermit to describe many biogeographical phenomena, as those of pollution, desertificationor epidemics, which are characterized by a spatio-temporal evolution

We discuss Laplacians on graphs in a framework of regular Dirichlet forms. We focus onphenomena related to unboundedness of the Laplacians. This includes (failure of) essentialselfadjointness, absence of essential spectrum and stochastic incompleteness.

In this paper, a new a posteriori error estimator for nonconforming convection diffusionapproximation problem, which relies on the small discrete problems solution in stars, hasbeen established. It is equivalent to the energy error up to data oscillation without anysaturation assumption nor comparison with residual estimator

The aim of this paper is to study the effect of vibrations on convective instability ofreaction fronts in porous media. The model contains reaction-diffusion equations coupledwith the Darcy equation. Linear stability analysis is carried out and the convectiveinstability boundary is found. The results are compared with direct numericalsimulations.

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.

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.