@inproceedings{12976,
  abstract     = {3D printing based on continuous deposition of materials, such as filament-based 3D printing, has seen widespread adoption thanks to its versatility in working with a wide range of materials. An important shortcoming of this type of technology is its limited multi-material capabilities. While there are simple hardware designs that enable multi-material printing in principle, the required software is heavily underdeveloped. A typical hardware design fuses together individual materials fed into a single chamber from multiple inlets before they are deposited. This design, however, introduces a time delay between the intended material mixture and its actual deposition. In this work, inspired by diverse path planning research in robotics, we show that this mechanical challenge can be addressed via improved printer control. We propose to formulate the search for optimal multi-material printing policies in a reinforcement
learning setup. We put forward a simple numerical deposition model that takes into account the non-linear material mixing and delayed material deposition. To validate our system we focus on color fabrication, a problem known for its strict requirements for varying material mixtures at a high spatial frequency. We demonstrate that our learned control policy outperforms state-of-the-art hand-crafted algorithms.},
  author       = {Liao, Kang and Tricard, Thibault and Piovarci, Michael and Seidel, Hans-Peter and Babaei, Vahid},
  booktitle    = {2023 IEEE International Conference on Robotics and Automation},
  issn         = {1050-4729},
  keywords     = {reinforcement learning, deposition, control, color, multi-filament},
  location     = {London, United Kingdom},
  pages        = {12345--12352},
  publisher    = {IEEE},
  title        = {{Learning deposition policies for fused multi-material 3D printing}},
  doi          = {10.1109/ICRA48891.2023.10160465},
  volume       = {2023},
  year         = {2023},
}

@article{11343,
  abstract     = {Multistable systems are characterized by exhibiting domain coexistence, where each domain accounts for the different equilibrium states. In case these systems are described by vectorial fields, domains can be connected through topological defects. Vortices are one of the most frequent and studied topological defect points. Optical vortices are equally relevant for their fundamental features as beams with topological features and their applications in image processing, telecommunications, optical tweezers, and quantum information. A natural source of optical vortices is the interaction of light beams with matter vortices in liquid crystal cells. The rhythms that govern the emergence of matter vortices due to fluctuations are not established. Here, we investigate the nucleation mechanisms of the matter vortices in liquid crystal cells and establish statistical laws that govern them. Based on a stochastic amplitude equation, the law for the number of nucleated vortices as a function of anisotropy, voltage, and noise level intensity is set. Experimental observations in a nematic liquid crystal cell with homeotropic anchoring and a negative anisotropic dielectric constant under the influence of a transversal electric field show a qualitative agreement with the theoretical findings.},
  author       = {Aguilera, Esteban and Clerc, Marcel G. and Zambra, Valeska},
  issn         = {1573-269X},
  journal      = {Nonlinear Dynamics},
  keywords     = {Electrical and Electronic Engineering, Applied Mathematics, Mechanical Engineering, Ocean Engineering, Aerospace Engineering, Control and Systems Engineering},
  pages        = {3209--3218},
  publisher    = {Springer Nature},
  title        = {{Vortices nucleation by inherent fluctuations in nematic liquid crystal cells}},
  doi          = {10.1007/s11071-022-07396-5},
  volume       = {108},
  year         = {2022},
}

@article{11683,
  abstract     = {The vertex connectivity κ of a graph is the smallest number of vertices whose deletion separates the graph or makes it trivial. We present the fastest known deterministic algorithm for finding the vertex connectivity and a corresponding separator. The time for a digraph having n vertices and m edges is O(min{κ3 + n, κn}m); for an undirected graph the term m can be replaced by κn. A randomized algorithm finds κ with error probability 1/2 in time O(nm). If the vertices have nonnegative weights the weighted vertex connectivity is found in time O(κ1nmlog(n2/m)) where κ1 ≤ m/n is the unweighted vertex connectivity or in expected time O(nmlog(n2/m)) with error probability 1/2. The main algorithm combines two previous vertex connectivity algorithms and a generalization of the preflow-push algorithm of Hao and Orlin (1994, J. Algorithms17, 424–446) that computes edge connectivity.},
  author       = {Henzinger, Monika H and Rao, Satish and Gabow, Harold N.},
  issn         = {0196-6774},
  journal      = {Journal of Algorithms},
  keywords     = {Computational Theory and Mathematics, Computational Mathematics, Control and Optimization},
  number       = {2},
  pages        = {222--250},
  publisher    = {Elsevier},
  title        = {{Computing vertex connectivity: New bounds from old techniques}},
  doi          = {10.1006/jagm.1999.1055},
  volume       = {34},
  year         = {2000},
}