Related papers: Computer-Assisted Proofs for Geometric Optimizatio…
Using carbon nanotubes (CNTs) produced by chemical vapor deposition, we have explored different strategies for the preparation of carbon nanotube devices suited for electrical and mechanical measurements. Though the target device is a…
Carbon nanotubes tend to collapse when their diameters exceed a certain threshold, or when a sufficiently large external pressure is applied on their walls. Their radial stability of tubes has been studied in each of these cases, however a…
This work addresses the classic machine learning problem of online prediction with expert advice. A new potential-based framework for the fixed horizon version of this problem has been recently developed using verification arguments from…
The electronic properties of carbon nanotubes are governed by their chirality, specified by the integer indices (n,m). While chirality-controlled synthesis has achieved notable successes, theoretical understanding remains predominantly…
The positions of atoms forming a carbon nanotube are usually described by using a system of generators of the symmetry group. Each atomic position corresponds to an element of the set Z X {0,1,...,n} X {0,1}, where n is a natural number…
We develop a general framework for the probabilistic analysis of random finite point clouds in the context of topological data analysis. We extend the notion of a barcode of a finite point cloud to compact metric spaces. Such a barcode…
Understanding how complex systems transition between states requires mapping the energy landscape that governs these changes. Local transition-state networks reveal the barrier architecture that explains observed behaviour and enables…
Optimization-based methods are commonly applied in autonomous driving trajectory planners, which transform the continuous-time trajectory planning problem into a finite nonlinear program with constraints imposed at finite collocation…
Optimization of frame structures is formulated as a~non-convex optimization problem, which is currently solved to local optimality. In this contribution, we investigate four optimization approaches: (i) general non-linear optimization, (ii)…
Methodologies for reducing the design-space dimensionality in shape optimization have been recently developed based on unsupervised machine learning methods. These methods provide reduced dimensionality representations of the design space,…
We consider the problem of optimal approximation of a target measure by an atomic measure with $N$ atoms, in branched optimal transport distance. This is a new branched transport version of optimal quantization problems. New difficulties…
The electronic states of capped semi-infinite nanotubes are studied within the phenomenological gauge field-theory model. A single manifold for the description of both the nanotube and the cap region (considered as nearly a half of either…
Structured optimization problems are ubiquitous in fields like data science and engineering. The goal in structured optimization is using a prescribed set of points, called atoms, to build up a solution that minimizes or maximizes a given…
This paper presents a detailed study of constrained quantization for both finite and infinite discrete probability distributions supported on subsets of the real line. Under specific geometric constraints - namely, a semicircular arc and…
Alternating minimization heuristics seek to solve a (difficult) global optimization task through iteratively solving a sequence of (much easier) local optimization tasks on different parts (or blocks) of the input parameters. While popular…
In this paper, we propose a descent method for composite optimization problems with linear operators. Specifically, we first design a structure-exploiting preconditioner tailored to the linear operator so that the resulting preconditioned…
Scanning Surface Potential Microscopy (SSPM) is one of the most widely used techniques for the characterization of electrical properties at small dimensions. Applicability of SSPM and related electrostatic scanning probe microscopies for…
Let $G$ be a connected reductive group acting on a complex vector space $V$ and projective space ${\mathbb P}V$. Let $x\in V$ and ${\cal H}\subseteq {\cal G}$ be the Lie algebra of its stabilizer. Our objective is to understand points…
A pristine suspended carbon nanotube is a near ideal environment to host long-lived quantum states. For this reason, they have been used as the core element of qubits and to explore numerous condensed matter physics phenomena. One of the…
We study black-box optimization of Lipschitz functions under noisy evaluations. Existing adaptive discretization methods implicitly avoid suboptimal regions but do not provide explicit certificates of optimality or measurable progress…