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A general topic of current interest is the analysis of diffusion problems in singularly perturbed domains with small interior targets or traps (the narrow capture problem). One major application is to intracellular diffusion, where the…
This paper connects discrete optimal transport to a certain class of multi-objective optimization problems. In both settings, the decision variables can be organized into a matrix. In the multi-objective problem, the notion of Pareto…
Grating magneto-optical traps are an enabling quantum technology for portable metrological devices with ultracold atoms. However, beam diffraction efficiency and angle are affected by wavelength, creating a single-optic design challenge for…
Disordered nanostructures are commonly encountered in many nanophotonic systems, from colloid dispersions for sensing, to heterostructured photocatalysts. Randomness, however, imposes severe challenges for nanophotonics modeling, often…
In this work we are interested in stochastic particle methods for multi-objective optimization. The problem is formulated using parametrized, single-objective sub-problems which are solved simultaneously. To this end a consensus based…
With the emergence of new photonic and plasmonic materials with optimized properties as well as advanced nanofabrication techniques, nanophotonic devices are now capable of providing solutions to global challenges in energy conversion,…
We present a novel adaptive optimization algorithm for black-box multi-objective optimization problems with binary constraints on the foundation of Bayes optimization. Our method is based on probabilistic regression and classification…
The subject of low energy photon-photon scattering is considered in arbitrary dimensional space-time and the interaction is widened to include scattering events involving an arbitrary number of photons. The effective interaction Lagrangian…
Scatterometry is a tested method for measuring periodic semiconductor structures. Since the sizes of modern semiconductor structures have reached the nanoscale regime, the challenge is to determine the shape of periodic nanostructures with…
A new algorithm for solving large-scale convex optimization problems with a separable objective function is proposed. The basic idea is to combine three techniques: Lagrangian dual decomposition, excessive gap and smoothing. The main…
Multi-objective optimization aims at finding trade-off solutions to conflicting objectives. These constitute the Pareto optimal set. In the context of expensive-to-evaluate functions, it is impossible and often non-informative to look for…
Optical tweezers enable non-contact trapping of micro-scale objects using light. Despite their widespread use, it is currently not known how tightly it is possible to three-dimensionally trap micro-particles with a given photon budget.…
Lagrangian duality in mixed integer optimization is a useful framework for problems decomposition and for producing tight lower bounds to the optimal objective, but in contrast to the convex counterpart, it is generally unable to produce…
In this paper we characterize sharp time-data tradeoffs for optimization problems used for solving linear inverse problems. We focus on the minimization of a least-squares objective subject to a constraint defined as the sub-level set of a…
Nervous systems, like any organismal structure, have been shaped by evolutionary processes to increase fitness. The resulting neural 'bauplan' has to account for multiple objectives simultaneously, including computational function as well…
We consider a particle undergoing diffusion with stochastic resetting in a bounded domain $\calU\subset \R^d$ for $d=2,3$. The domain is perforated by a set of partially absorbing targets within which the particle may be absorbed at a rate…
This work studies the inverse boundary problem for the two photon absorption radiative transport equation. We show that the absorption coefficients and scattering coefficients can be uniquely determined from the \emph{albedo} operator. If…
We study embedding a subset $K$ of the unit sphere to the Hamming cube $\{-1,+1\}^m$. We characterize the tradeoff between distortion and sample complexity $m$ in terms of the Gaussian width $\omega(K)$ of the set. For subspaces and several…
We introduce in this document a direct method allowing to solve numerically inverse type problems for linear parabolic equations. We consider the reconstruction of the full solution of the parabolic equation posed in $\Omega\times (0,T)$ -…
Light reflection plays a crucial role in a number of modern technologies. In this paper, analytical expressions for maximal reflected power in any direction and for any polarization are given for generic planar structures made of a single…