Approximating Pareto curves using semidefinite relaxations

We approximate as closely as desired the Pareto curve associated with bicriteria polynomial optimization problems. We use three formulations (including the weighted sum approach and the Chebyshev approximation) and each of them is viewed as a parametric polynomial optimization problem. For each case is associated a hierarchy of semidefinite relaxations and from an optimal solution of each relaxation one approximates the Pareto curve by solving an inverse problem (first two cases) or by building a polynomial underestimator (third case).     

Tractability results for the weighted star-discrepancy

The weighted star-discrepancy has been introduced by Sloan and Wo?niakowski to reflect the fact that in multidimensional integration problems some coordinates of a function may be more important than others. It provides upper bounds for the error of multidimensional numerical integration algorithms for functions belonging to weighted function spaces of Sobolev type. In the present paper, we prove several tractability results for the weighted star-discrepancy. In particular, we obtain rather sharp sufficient conditions under which the weighted star-discrepancy is strongly tractable. The proofs are probabilistic, and use empirical process theory.     

Preparation and characterization of carbon aerogel microspheres by an inverse emulsion polymerization

Carbon aerogel (CA) microspheres have been successfully synthesized by an inverse emulsion polymerization and characterized by scanning electron microscopy (SEM), N₂ sorption isotherm and X-ray diffraction (XRD). The results show that the size and pore characteristics of carbon microsphere obviously depend on stirring speed and concentration of surfactant in the emulsion polymerization process. The resultant CA microspheres are amorphous carbon structure with the size ranging from about 2 to 50 μm by changing the stirring speed. CA microspheres with S_BET of 414-603 m² g^− 1 and V_meso of 0.028-0.432 cm³ g^− 1 are synthesized using different SPAN80 concentrations. The results of cyclic voltammetry indicate that the CA microspheres prepared at a stirring speed of 480 rpm and at V_s/V_h = 0.01 have ideal supercapacitive behavior in 6 M KOH electrolyte, the maximum specific capacitance of the electrode reaches 180 F g^− 1.     

Inverse problem for the reaction diffusion system by optimization method

In this paper, we study an inverse problem of reconstructing two time independent coefficients in the reaction diffusion system from the final measurement. First the given problem is transformed into an optimization problem by using optimal control framework and the existence of the minimizer for the control functional is established. Then we prove the stability estimate for two coefficients with the upper bound given by some Sobolev norms of the final measurement.     

A behavior-oriented model for long-term coastal profile evolution: Validation,identification, and prediction

A behavior-oriented diffusion model, governing the time evolution of the cross-shore position of coastal profiles, is studied. Here, two time-independent, space-varying coefficients, which embody the relevant physical properties, are identified simultaneously. Two sets of real data, the first measured over 10 years at Duck, in NC (USA), the second obtained over 39 years measurements at Delfland (Holland), have been processed numerically by a suitable “inversion algorithm”, earlier developed by the authors. This is based on the minimization of a certain cost functional in order to identify both coefficients. The numerical results, obtained by solving the diffusion equation with the so-determined coefficients, favorably agree with the real data, which fact validates and calibrates somehow the diffusion model under investigation. A short-term prediction is finally obtained for coastal profiles, using such a model.     

Optimal control of self-organized dynamics in cellular signal transduction

We demonstrate how model-based optimal control can be exploited in biological and biochemical modelling applications in several ways. In the first part, we apply optimal control to a detailed kinetic model of a glycolysis oscillator, which plays a central role in immune cells, in order to analyse potential regulatory mechanisms in the dynamics of associated signalling pathways. We demonstrate that the formulation of inverse problems with the aim to determine specific time-dependent input stimuli can provide important insight into dynamic regulations of self-organized cellular signal transduction. In the second part, we present an optimal control study aimed at target-oriented manipulation of a biological rhythm, an internal clock mechanism related to the circadian oscillator. This oscillator is responsible for the approximate endogenous 24 h (latin: circa dies) day-night rhythm in many organisms. On the basis of a kinetic model for the fruit fly Drosophila, we compute switching light stimuli via mixed-integer optimal control that annihilate the oscillations for a fixed time interval. Insight gained from such model-based specific manipulation may be promising in biomedical applications.     

Observation of inverse sawtooth activity on central soft X-ray emission during impurity injection in the J-TEXT tokamak

Short- and long-time lasting inverse sawtooth activities during neon (Ne) gas injection, not during helium (He) or argon (Ar) though, have been clearly observed on soft X-ray emissions from chords viewing the central plasma region of the Joint Texas Experimental Tokamak (J-TEXT). A self-consistent interpretation of the inverse sawtooth activity depending on the impurity radiation characteristics is proposed. It is evidenced that the radiation loss caused by the injection of noble gas not only depends on the amount of the noble gas itself, but also depends on the temperature region where the noble gas can reach.     

Fine-tuning inverse metal-support interaction boosts electrochemical transformation of methanol into formaldehyde based on density functional theory

Different from traditional metal-support heterogenous catalysts,inverse heterogeneous catalysts,in which the surface of metal is decorated by metal oxide,have recently attracted increasing interests owing to the unique interracial effect and electronic structure.However,a deep insight into the effect of metaloxide interaction on the catalytic performance still remains a great challenge.In our work,an inverse hematite/palladium(Fe_2 O_3/Pd) hybrid nanostructure,i.e.,the active Fe_2 O_3 ultrathin oxide layers partially covering on the surface of Pd nanoparticles(NPs),exhibited superior electrocatalytic performance towards methanol oxidation reaction(MOR) as compared to the bare Pd NPs based on density functional theory calculation.The charge could transfer from Pd to Fe_2 O_3 driven by the built-in potential at the interface of Pd and Fe_2 O_3,which favors the downshift of d band center of Pd.With the assistance of interfacial hydroxyl OH~*,the cleavage of O—H and C—H in CH_3 OH could take place much easily with lower barrier ene rgy on Fe_2 O_3/Pd than that on pure Pd via two electrons transferring reaction pathways.Our results highlight that the syne rgy of Pd and Fe_2 O_3 at the interface could facilitate the electrochemical transformation of methanol into formaldehyde assisted with interfacial hydroxyl OH~*.     

Identifiability at the boundary for first-order terms

Let Ω be a domain in R ⁿ whose boundary is C ¹ if n≥3 or C ^1,β if n=2. We consider a magnetic Schrödinger operator L _{W , q} in Ω and show how to recover the boundary values of the tangential component of the vector potential W from the Dirichlet to Neumann map for L _{W , q} . We also consider a steady state heat equation with convection term Δ+2W·? and recover the boundary values of the convection term W from the Dirichlet to Neumann map. Our method is constructive and gives a stability result at the boundary.