Optimal transport and a bilevel location-allocation problem

In this paper a two-stage optimization model is studied to find the optimal location of new facilities and the optimal partition of the consumers (location-allocation problem). The social planner minimizes the social costs, i.e. the fixed costs plus the waiting time costs, taking into account that the citizens are partitioned in the region according to minimizing the capacity costs plus the distribution costs in the service regions. By using optimal transport tools, existence results of solutions to the location-allocation problem are presented together with some examples.     

Approximate equilibria for Bayesian games

In this paper the problem of the existence of approximate equilibria in mixed strategies is central. Sufficient conditions are given under which approximate equilibria exist for non-finite Bayesian games. Further one possible approach is suggested to the problem of the existence of approximate equilibria for the class of multicriteria Bayesian games.     

Magnetoelectric effect in cobalt ferrite-barium titanate composites and their electrical properties

CoFe₂O₄-BaTiO₃ composites were prepared using conventional ceramic double sintering process with various compositions. Presence of two phases in the composites was confirmed using X-ray diffraction. The dc resistivity and thermoemf as a function of temperature in the temperature range 300 K to 600 K were measured. Variation of dielectric constant (ɛ′) with frequency in the range 100 Hz to 1 MHz and also with temperature at a fixed frequency of 1 kHz was studied. The ac conductivity was derived from dielectric constant (ɛ′) and loss tangent (tan δ). The nature of conduction is discussed on the basis of small polaron hopping model. The static value of magnetoelectric conversion factor has been studied as a function of magnetic field.     

Making MRI quieter

We have mitigated acoustic noise in a 1.5 T cylindrical MRI scanner equipped with epoxy-potted, shielded gradients. It has been widely assumed that MRI acoustic noise comes overwhelmingly from vibrations of the gradient assembly. However, with vibration-isolated gradients contained in an airtight enclosure, we found the primary sources of acoustic noise to be eddy-current-induced vibrations of metal structures such as the cryostat inner bore and the rf body coil. We have elucidated the relative strengths of source-pathways of acoustic noise and assembled a reduced-acoustic-noise demonstration MRI system. This scanner employed a number of acoustic noise reduction measures including a vacuum enclosure of a vibrationally isolated gradient assembly, a low-eddy-current rf coil and a non-conducting inner bore cryostat. The demonstration scanner reduced, by about 20 dBA, the acoustic noise levels in the patient bore to 85 dBA and below for several typical noisy pulse sequences. The noise level standing near the patient bore is 71 dBA and below. We have applied Statistical Energy Analysis to develop a vibroacoustic model of the MR system. Our model includes vibrational sources and acoustic pathways to predict acoustic noise and provides a good spectral match above 400 Hz to experimentally measured sound levels. This tool enables us to factor acoustics into the design parameters of new MRI systems.     

Softening Bilevel Problems Via Two-scale Gibbs Measures

We introduce a new, and elementary, approximation method for bilevel optimization problems motivated by Stackelberg leader-follower games. Our technique is based on the notion of two-scale Gibbs measures. The first scale corresponds to the cost function of the follower and the second scale to that of the leader. We explain how to choose the weights corresponding to these two scales under very general assumptions and establish rigorous Γ-convergence results. An advantage of our method is that it is applicable both to optimistic and to pessimistic bilevel problems.

     

ɛ-Mixed strategies for static continuous-kernel stackelberg games

We consider a two-level optimization problem corresponding to a Stackelberg game in which the response function of the follower is multivalued and some convexity assumption on the data is missing. Different notions of -mixed strategies are introduced and sufficient conditions on the data for existence and convergence of the corresponding average values, as converges to 0, are given together with several examples.This paper is based upon results first presented at the International Conference on Game Theory, Firenze, Italia, 1991. This research has been supported by MPI, Roma, Italia.