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Finding diverse solutions to optimization problems has been of practical interest for several decades, and recently enjoyed increasing attention in research. While submodular optimization has been rigorously studied in many fields, its…
Anomalous resonances in properly shaped plasmonic nanostructures can in principle lead to infinite absorption/gain efficiencies over broad bandwidths. By developing a closed-form analytical solution for the fields scattered by conjoined…
Electromagnetic scattering and absorption by material particles is a fundamental physical problem with a broad range of applications, going from laboratory experiments, biology and material sciences, all the way up to environmental studies…
Nanoscale fabrication techniques, computational inverse design, and fields from silicon photonics to metasurface optics are enabling transformative use of an unprecedented number of structural degrees of freedom in nanophotonics. A critical…
We study the optimization of the expected long-term reward in finite partially observable Markov decision processes over the set of stationary stochastic policies. In the case of deterministic observations, also known as state aggregation,…
Solutions to multi-objective optimization problems can generally not be compared or ordered, due to the lack of orderability of the single objectives. Furthermore, decision-makers are often made to believe that scaled objectives can be…
This work studies the limits of far and near-field electromagnetic response of sub-wavelength scatterers, like the unitary limit and of lossless scatterers, and the ideal absorption limit of lossy particles. These limit behaviors are…
We consider a new approach to the nucleon-nucleon scattering problem in the framework of the higher-derivative formulation of baryon chiral perturbation theory. Starting with a Lorentz-invariant form of the effective Lagrangian we work out…
Performance of reliable communication over a coherent slow fading channel at high SNR is succinctly captured as a fundamental tradeoff between diversity and multiplexing gains. We study the problem of designing codes that optimally tradeoff…
Ensuring user fairness in wireless communications is a fundamental challenge, as balancing the trade-off between fairness and sum rate leads to a non-convex, multi-objective optimization whose complexity grows with network scale. To…
We consider a class of finite element approximations for fourth-order parabolic equations that can be written as a system of second-order equations by introducing an auxiliary variable. In our approach, we first solve a variational problem…
When agents with independent priors bid for a single item, Myerson's optimal auction maximizes expected revenue, whereas Vickrey's second-price auction optimizes social welfare. We address the natural question of trade-offs between the two…
We use inverse methods of statistical mechanics to explore trade-offs associated with designing interactions to stabilize self-assembled structures against changes in density or temperature. Specifically, we find isotropic,convex-repulsive…
We consider the nucleon-nucleon scattering problem by applying time-ordered perturbation theory to the Lorentz invariant formulation of baryon chiral perturbation theory. Using a symmetry preserving higher derivative form of the effective…
A model for the adsorption of a binary mixture on a one-dimensional infinite lattice with nearest neighbour cooperative effects is considered. The particles of the two species are both monomers but differ in the repulsive interaction…
Understanding the relationships between objectives in a multiobjective optimisation problem is important for developing tailored and efficient solving techniques. In particular, when tackling combinatorial optimisation problems with many…
A boundary value problem is commonly associated with constraints imposed on a system at its boundary. We advance here an alternative point of view treating the system as interacting "boundary" and "interior" subsystems. This view is…
Efficiently solving multi-objective optimization problems for simulation optimization of important scientific and engineering applications such as materials design is becoming an increasingly important research topic. This is due largely to…
Scalarization allows to solve a multi-objective optimization problem by solving many single-objective sub-problems, uniquely determined by some parameters. In this work, we propose several adaptive strategies to select such parameters in…
Pareto-optimality plays a central role in evaluating the efficiency of solutions to allocation problems, such as house allocation, school choice, and kidney exchange. We introduce a general linear programming problem subject to…