Related papers: Ideal, best packing, and energy minimizing double …
Higher-dimensional orthogonal packing problems have a wide range of practical applications, including packing, cutting, and scheduling. Combining the use of our data structure for characterizing feasible packings with our new classes of…
A finite element program is presented to simulate the process of packing and coiling elastic wires in two- and three-dimensional confining cavities. The wire is represented by third order beam elements and embedded into a corotational…
The hydrophobic-polar (HP) model represents proteins as binary strings embedded in lattices, with fold quality measured by an energy score. We prove that the optimal fold energy is not monotonic under concatenation for several standard…
Many problems in science and engineering can be rigorously recast into minimizing a suitable energy functional. We have been developing efficient and flexible solution strategies to tackle various minimization problems by employing finite…
We investigate the packing and covering densities of linear and nonlinear binary codes, and establish a number of duality relationships between the packing and covering problems. Specifically, we prove that if almost all codes (in the class…
The paper describes the first exact results in optimal design of three-phase elastic structures. Two isotropic materials, the "strong" and the "weak" one, are laid out with void in a given two-dimensional domain so that the compliance plus…
We provide new answers about the placement of mass on spheres so as to minimize energies of pairwise interactions. We find optimal measures for the $p$-frame energies, i.e. energies with the kernel given by the absolute value of the inner…
Combing hair involves brushing away the topological tangles in a collective curl. Using a combination of experiment and computation, we study this problem that naturally links topology, geometry and mechanics. Observations show that the…
Three-point semidefinite programming bounds are one of the most powerful known tools for bounding the size of spherical codes. In this paper, we use them to prove lower bounds for the potential energy of particles interacting via a pair…
Consider the problem of constructing an experimental design, optimal for estimating parameters of a given statistical model with respect to a chosen criterion. To address this problem, the literature usually provides a single solution.…
Trapped ions offer long internal state (spin) coherence times and strong inter-particle interactions mediated by the Coulomb force. This makes them interesting candidates for quantum simulation of coupled lattices. To this end it is…
In this paper, we introduce methods from convex optimization to solve the multimarginal transport type problems arise in the context of density functional theory. Convex relaxations are used to provide outer approximation to the set of…
Optimal packing of spheres in $\mathbb R^d$ is studied by optimization of the energy $E$ (effective conductivity) of composites with ideally conducting spherical inclusions. It is demonstrated that the minimum of $E$ over locations of…
In this thesis I explore challenging discrete energy minimization problems that arise mainly in the context of computer vision tasks. This work motivates the use of such "hard-to-optimize" non-submodular functionals, and proposes methods…
A reduced model, which can fold both helix and sheet structures, is proposed to study the problem of protein folding. The goal of this model is to find an unbiased effective potential that has included the effects of water and at the same…
An approach to optimal actuator design based on shape and topology optimisation techniques is presented. For linear diffusion equations, two scenarios are considered. For the first one, best actuators are determined depending on a given…
We study optimal design problems for stationary diffusion involving one or more state equations and mixtures of an arbitrary number of anisotropic materials. Since such problems typically do not admit classical solutions, we adopt a…
We study measures and point configurations optimizing energies based on multivariate potentials. The emphasis is put on potentials defined by geometric characteristics of sets of points, which serve as multi-input generalizations of the…
Two proteins, one belonging to the mainly alpha class and the other belonging to the alpha/beta class, are selected to test a kinetic mechanism for protein folding. Targeted molecular dynamics is applied to generate folding pathways for…
We present a general analysis of exchange devices linking their efficiency to the geometry of the exchange surface and supply network. For certain parameter ranges, we show that the optimal exchanger consists of densely packed pipes which…