In this paper, an artificial neural network (ANN) based on hybrid algorithm combiningparticle swarm optimization (PSO) with back-propagation (BP) is proposed to forecast thedaily streamflows in a catchment located in a semi-arid region in Morocco. The PSOalgorithm has a rapid convergence during the initial stages of a global search, while theBP algorithm can achieve faster convergent speed around the global optimum. By combiningthe PSO with the BP, the hybrid algorithm referred to as BP-PSO algorithm is presented inthis paper. To evaluate the performance of the hybrid algorithm, BP neural network is alsoinvolved for a comparison purposes. The results show that the neural network model evolvedby PSO-BP algorithm has a good predictions and better convergence performances

Experimental evidence points to a rich variety of physical scenarios that arise when alaminar flame propagates through a pre-mixture of evaporating liquid fuel and a gaseousoxidant. In this paper new results of time-dependent numerical simulations of richoff-stoichiometric spray flame propagation in a two-dimensional channel are presented. Aconstant density model is adopted, thereby eliminating the Darrieus-Landau instability. Itis demonstrated that there exists a narrow band of vaporization Damkohler numbers (theratio of a characteristic flow time to a characteristic evaporation time) for which theflame propagation is oscillatory. For values outside this range steady state propagationis attained but with a curved (cellular) flame front. The critical range for thenon-steady propagation is also found to be a function of the Lewis number of the deficientreactant.

We study a class of bistable reaction-diffusion systems used to model two competingspecies. Systems in this class possess two uniform stable steady states representingsemi-trivial solutions. Principally, we are interested in the case where the ratio of thediffusion coefficients is small, i.e. in thenear-degenerate case. First, limiting arguments are presented to relatesolutions to such systems to those of the degenerate case where one species is assumed notto diffuse. We then consider travelling wave solutions that connect the two stablesemi-trivial states of the non-degenerate system. Next, a general energy function for thefull system is introduced. Using this and the limiting arguments, we are able to determinethe wave direction for small diffusion coefficient ratios. The results obtained onlyrequire knowledge of the system kinetics.

In this short note, we apply the technique developed in [Math. Model. Nat. Phenom., 5 (2010), No. 4, 122-149] to study the long-time evolution for Schrödinger equation with slowly decayingpotential.

We review some recent results for a class of fluid mechanics equations called activescalars, with fractional dissipation. Our main examples are the surface quasi-geostrophicequation, the Burgers equation, and the Cordoba-Cordoba-Fontelos model. We discussnonlocal maximum principle methods which allow to prove existence of global regularsolutions for the critical dissipation. We also recall what is known about the possibilityof finite time blow up in the supercritical regime.

We present a simple mechanism of cell motility in a confined geometry, inspired by recentmotility assays in microfabricated channels. This mechanism relies mainly on the couplingof actin polymerisation at the cell membrane to geometric confinement. We first showanalytically using a minimal model of polymerising viscoelastic gel confined in a narrowchannel that spontaneous motion occurs due to polymerisation alone. Interestingly, thismechanism does not require specific adhesion with the channel walls, and yields velocitiespotentially larger than the polymerisation velocity of the gel. We then study the effectof the contractile activity of myosin motors, and show that whilst it is not necessary toinduce motion, it quantitatively increases the velocity of motion in the polymerisationmechanism we describe. Our model qualitatively accounts for recent experiments which showthat cells without specific adhesion proteins are motile only in confined environmentswhile they are unable to move on a flat surface. It also constitutes a first step in thestudy of cell migration in more complex confined geometries such as living tissues.

In this work we study a nonlocal reaction-diffusion equation arising in populationdynamics. The integral term in the nonlinearity describes nonlocal stimulation ofreproduction. We prove existence of travelling wave solutions by the Leray-Schauder methodusing topological degree for Fredholm and proper operators and special a priori estimatesof solutions in weighted Hölder spaces.

In this paper, we will discuss the meshless polyharmonic reconstruction of vector fieldsfrom scattered data, possibly, contaminated by noise. We give an explicit solution of theproblem. After some theoretical framework, we discuss some numerical aspect arising in theproblems related to the reconstruction of vector fields

In this note, we consider a nonlinear diffusion equation with a bistable reaction termarising in population dynamics. Given a rather general initial data, we investigate itsbehavior for small times as the reaction coefficient tends to infinity: we prove ageneration of interface property.

Recent technological advances including brain imaging (higher resolution in space andtime), miniaturization of integrated circuits (nanotechnologies), and acceleration ofcomputation speed (Moore’s Law), combined with interpenetration between neuroscience,mathematics, and physics have led to the development of more biologically plausiblecomputational models and novel therapeutic strategies. Today, mathematical models ofirreversible medical conditions such as Parkinson’s disease (PD) are developed andparameterised based on clinical data. How do these evolutions have a bearing on deep brainstimulation (DBS) of patients with PD? We review how the idea of DBS, a standardtherapeutic strategy used to attenuate neurological symptoms (motor, psychiatric), hasemerged from past experimental and clinical observations, and present how, over the lastdecade, computational models based on different approaches (phase oscillator models,spiking neuron network models, population-based models) have started to shed light ontoDBS mechanisms. Finally, we explore a new mathematical modelling approach based on neuralfield equations to optimize mechanisms of brain stimulation and achieve finer control oftargeted neuronal populations. We conclude that neuroscience and mathematics are crucialpartners in exploring brain stimulation and this partnership should also include otherdomains such as signal processing, control theory and ethics.

We derive a residual a posteriori error estimates for the subscales stabilization ofconvection diffusion equation. The estimator yields upper bound on the error which isglobal and lower bound that is local

It is shown that a real Hankel matrix admits an approximate block diagonalization inwhich the successive transformation matrices are upper triangular Toeplitz matrices. Thestructure of this factorization was first fully discussed in [1]. This approach isextended to obtain the quotients and the remainders appearing in the Euclidean algorithmapplied to two polynomials u(x) andv(x) of degree n andm, respectively, whith m <n

In L 2(ℝd ;ℂn ), we consider a wide class of matrix elliptic secondorder differential operators $\mathcal{A}$ εwith rapidly oscillating coefficients (depending on x/ε).For a fixed τ > 0 and small ε > 0, we findapproximation of the operator exponential exp(− $\mathcal{A}$ ε τ) in the(L 2(ℝd ;ℂn ) →H 1(ℝd ;ℂn ))-operator norm with an error term of orderε. In this approximation, the corrector is taken into account. Theresults are applied to homogenization of a periodic parabolic Cauchy problem.

We provide a systematic study of boundary data maps, that is, 2 × 2 matrix-valuedDirichlet-to-Neumann and more generally, Robin-to-Robin maps, associated withone-dimensional Schrödinger operators on a compact interval [0, R] withseparated boundary conditions at 0 and R. Most of our results areformulated in the non-self-adjoint context.

Our principal results include explicit representations of these boundary data maps interms of the resolvent of the underlying Schrödinger operator and the associated boundarytrace maps, Krein-type resolvent formulas relating Schrödinger operators corresponding todifferent (separated) boundary conditions, and a derivation of the Herglotz property ofboundary data maps (up to right multiplication by an appropriate diagonal matrix) in thespecial self-adjoint case.

The CDC launched the National Plan to Eliminate Syphilis from the USA in October 1999[4]. In order to reach this goal, a goodunderstanding of the transmission dynamics of the disease is necessary. Based on a SIRSmodel Breban et al. [3] providedsome evidence that supports the feasibility of the plan proving that no recurringoutbreaks should occur for syphilis. We study in this work a syphilis model that includespartial immunity and vaccination. This model suggests that a backward bifurcation verylikely occurs for the real-life estimated epidemiological parameters for syphilis. Thismay explain the resurgence of syphilis after mass treatment [21]. Occurrence of backward bifurcation brings a new challenge for theplan of the CDC’s –striking a balance between treatment of early infection, vaccinationdevelopment and health education. Our models suggest that the development of an effectivevaccine, as well as health education that leads to enhanced biological and behavioralprotection against infection in high-risk populations, are among the best ways to achievethe goal of elimination of syphilis in the USA.

A simple model of biological evolution of community food webs is introduced. This modelis based on the niche model, which is known to generate model food webs that are verysimilar to empirical food webs. The networks evolve by speciation and extinction.Co-extinctions due to the loss of all prey species are found to play a major role indetermining the longterm shape of the food webs. The central aim is to design the modelsuch that the characteristic parameters of the niche model food webs remain in realisticintervals. When the mutation rule is chosen accordingly, it is found that food webs with acomplex, biologically meaningful structure emerge and that the statistics of extinctionevents agrees well with that observed in the paleontological data.

This work concerns an enlarged analysis of the problem of asymptotic compensation for aclass of discrete linear distributed systems. We study the possibility of asymptoticcompensation of a disturbance by bringing asymptotically the observation in a giventolerance zone 𝒞. Under convenient hypothesis, we show the existence and theunicity of the optimal control ensuring this compensation and we give itscharacterization

Background: Community-acquired methicillin-resistant Staphylococcusaureus (CA-MRSA), a novel strain of MRSA, has recently emerged and rapidlyspread in the community. Invasion into the hospital setting with replacement of thehospital-acquired MRSA (HA-MRSA) has also been documented. Co-colonization with bothCA-MRSA and HA-MRSA would have important clinical implications given differences inantimicrobial susceptibility profiles and the potential for exchange of geneticinformation.

Methods: A deterministic mathematical model was developed to characterizethe transmission dynamics of HA-MRSA and CA-MRSA in the hospital setting and to quantifythe emergence of co-colonization with both strains

Results: The model analysis shows that the state of co-colonization becomesendemic over time and that typically there is no competitive exclusion of either strain.Increasing the length of stay or rate of hospital entry among patients colonized withCA-MRSA leads to a rapid increase in the co-colonized state. Compared to MRSAdecolonization strategy, improving hand hygiene compliance has the greatest impact ondecreasing the prevalence of HA-MRSA, CA-MRSA and the co-colonized state.

Conclusions: The model predicts that with the expanding community reservoirof CA-MRSA, the majority of hospitalized patients will become colonized with both CA-MRSAand HA-MRSA.

Over the past decade or so, there have been a large number of modelling approaches aimedat elucidating the most important mechanisms affecting the formation of new capillariesfrom parent blood vessels — a process known as angiogenesis. Most studies have focussedupon the way in which capillary sprouts are initiated and migrate in response todiffusible chemical stimuli supplied by hypoxic stromal cells and leukocytes in thecontexts of solid tumour growth and wound healing. However, relatively few studies haveexamined the important role played by blood perfusion during angiogenesis and fewer stillhave explored the ways in which a dynamically evolving vascular bed architecture canaffect the distribution of flow within it. From the perspective of solid tumour growthand, perhaps more importantly, its treatment (e.g. chemotherapy), it would clearly be ofsome benefit to understand this coupling between vascular structure and perfusion morefully. This paper focuses on the implications of such a coupling upon chemotherapeutic,anti-angiogenic, and anti-vascular treatments.

In an extension to previous work by the authors, the issue of pericyte recruitment duringvessel maturation is considered in order to study the effects of different anti-vascularand anti-angiogenic therapies from a more rigorous modelling standpoint. Pericytes are aprime target for new vascular disrupting agents (VDAs) currently in clinical trials.However, different compounds attack different components of the vascular network and theimplications of targeting only certain elements of the capillary bed are not immediatelyclear. In light of these uncertainties, the effects of anti-angiogenic and anti-vasculardrugs are re-examined by using an extended model that includes an interdependency betweenvessel remodelling potential and local pericyte density. Two- and three-dimensionalsimulation results are presented and suggest that it may be possible to identify aVDA-specific “plasticity window” (a time period corresponding to low pericyte density),within which a given VDA would be most effective.

We study the number of lattice points in ℝd ,d ≥ 2, lying inside an annulus as a function of the centre of theannulus. The average number of lattice points there equals the volume of the annulus, andwe study the L 1 and L 2 norms ofthe remainder. We say that a dimension is critical, if these norms do not have upper andlower bounds of the same order as the radius goes to infinity. In [Duke Math. J., 107 (2001), No. 2, 209–238], it was proved that in the case of the ball (instead of an annulus)the critical dimensions are d ≡ 1 mod 4. We show that the behaviour ofthe width of an annulus as a function of the radius determines which dimensions arecritical now. In particular, if the width is bounded away from zero and infinity, thecritical dimensions are d ≡ 3 mod 4; if the width goes to infinity, butslower than the radius, then all dimensions are critical, and if the width tends to zeroas a power of the radius, then there are no critical dimensions.