| 1. |
- Abrahamsen, Mikkel, et al.
(författare)
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Minimum Star Partitions of Simple Polygons in Polynomial Time
- 2024
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Ingår i: STOC 2024 - Proceedings of the 56th Annual ACM Symposium on Theory of Computing. - : Association for Computing Machinery (ACM). ; , s. 904-910
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Konferensbidrag (refereegranskat)abstract
- We devise a polynomial-time algorithm for partitioning a simple polygon P into a minimum number of star-shaped polygons. The question of whether such an algorithm exists has been open for more than four decades [Avis and Toussaint, Pattern Recognit., 1981] and it has been repeated frequently, for example in O'Rourke's famous book [Art Gallery Theorems and Algorithms, 1987]. In addition to its strong theoretical motivation, the problem is also motivated by practical domains such as CNC pocket milling, motion planning, and shape parameterization. The only previously known algorithm for a non-trivial special case is for P being both monotone and rectilinear [Liu and Ntafos, Algorithmica, 1991]. For general polygons, an algorithm was only known for the restricted version in which Steiner points are disallowed [Keil, SIAM J. Comput., 1985], meaning that each corner of a piece in the partition must also be a corner of P. Interestingly, the solution size for the restricted version may be linear for instances where the unrestricted solution has constant size. The covering variant in which the pieces are star-shaped but allowed to overlap - known as the Art Gallery Problem - was recently shown to be ∃ℝ-complete and is thus likely not in NP [Abrahamsen, Adamaszek and Miltzow, STOC 2018 & J. ACM 2022]; this is in stark contrast to our result. Arguably the most related work to ours is the polynomial-time algorithm to partition a simple polygon into a minimum number of convex pieces by Chazelle and Dobkin [STOC, 1979 & Comp. Geom., 1985].
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| 2. |
- Benabdallah, Nadia, et al.
(författare)
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Beyond Average : a-Particle Distribution and Dose Heterogeneity in Bone Metastatic Prostate Cancer
- 2024
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Ingår i: Journal of Nuclear Medicine. - 0161-5505. ; 65:2, s. 245-251
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Tidskriftsartikel (refereegranskat)abstract
- a-particle emitters are emerging as a potent modality for disseminated cancer therapy because of their high linear energy transfer and localized absorbed dose profile. Despite great interest and pharmaceutical development, there is scant information on the distribution of these agents at the scale of the a-particle pathlength. We sought to determine the distribution of clinically approved [223Ra]RaCl2 in bone metastatic castration-resistant prostate cancer at this resolution, for the first time to our knowledge, to inform activity distribution and dose at the near-cell scale. Methods: Biopsy specimens and blood were collected from 7 patients 24 h after administration. 223Ra activity in each sample was recorded, and the microstructure of biopsy specimens was analyzed by micro-CT. Quantitative autoradiography and histopathology were segmented and registered with an automated procedure. Activity distributions by tissue compartment and dosimetry calculations based on the MIRD formalism were performed. Results: We revealed the activity distribution differences across and within patient samples at the macro- and microscopic scales. Microdistribution analysis confirmed localized high-activity regions in a background of low-activity tissue. We evaluated heterogeneous a-particle emission distribution concentrated at bone–tissue interfaces and calculated spatially nonuniform absorbed-dose profiles. Conclusion: Primary patient data of radiopharmaceutical therapy distribution at the small scale revealed that 223Ra uptake is nonuniform. Dose estimates present both opportunities and challenges to enhance patient outcomes and are a first step toward personalized treatment approaches and improved understanding of a-particle radiopharmaceutical therapies.
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| 3. |
- Lindemann, Lars, et al.
(författare)
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Learning Hybrid Control Barrier Functions from Data
- 2020
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Ingår i: Proceedings of the 2020 Conference on Robot Learning, CoRL 2020. - : ML Research Press. ; , s. 1351-1370
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Konferensbidrag (refereegranskat)abstract
- Motivated by the lack of systematic tools to obtain safe control laws for hybrid systems, we propose an optimization-based framework for learning certifiably safe control laws from data. In particular, we assume a setting in which the system dynamics are known and in which data exhibiting safe system behavior is available. We propose hybrid control barrier functions for hybrid systems as a means to synthesize safe control inputs. Based on this notion, we present an optimization-based framework to learn such hybrid control barrier functions from data. Importantly, we identify sufficient conditions on the data such that feasibility of the optimization problem ensures correctness of the learned hybrid control barrier functions, and hence the safety of the system. We illustrate our findings in two simulations studies, including a compass gait walker.
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| 4. |
- Robey, Alexander, et al.
(författare)
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Learning Control Barrier Functions from Expert Demonstrations
- 2020
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Ingår i: 2020 59Th IEEE Conference On Decision And Control (Cdc). - : IEEE. ; , s. 3717-3724
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Konferensbidrag (refereegranskat)abstract
- Inspired by the success of imitation and inverse reinforcement learning in replicating expert behavior through optimal control, we propose a learning based approach to safe controller synthesis based on control barrier functions (CBFs). We consider the setting of a known nonlinear control affine dynamical system and assume that we have access to safe trajectories generated by an expert - a practical example of such a setting would be a kinematic model of a self-driving vehicle with safe trajectories (e.g., trajectories that avoid collisions with obstacles in the environment) generated by a human driver. We then propose and analyze an optimization based approach to learning a CBF that enjoys provable safety guarantees under suitable Lipschitz smoothness assumptions on the underlying dynamical system. A strength of our approach is that it is agnostic to the parameterization used to represent the CBF, assuming only that the Lipschitz constant of such functions can be efficiently bounded. Furthermore, if the CBF parameterization is convex, then under mild assumptions, so is our learning process. We end with extensive numerical evaluations of our results on both planar and realistic examples, using both random feature and deep neural network parameterizations of the CBF. To the best of our knowledge, these are the first results that learn provably safe control barrier functions from data.
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| 5. |
- Wei, Shuhe, et al.
(författare)
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Polypeptide-based vapor-responsive porous poly(ionic liquid) actuators : From reversible to unexpectedly irreversible actuation
- 2023
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Ingår i: Materials Today Communications. - : Elsevier BV. - 2352-4928. ; 35
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Tidskriftsartikel (refereegranskat)abstract
- Soft actuators capable of large and swift locomotion in combination with biocompatibility hold great potential in medicine and healthcare applications. In this contribution, a polypeptide-type poly(ionic liquid) (termed “PLL-PMIM-Tf2N”) was designed and synthesized by post-polymerization modification of poly-L-lysine; Next, via controlled electrostatic complexation with poly(acrylic acid) (PAA) or poly(L-glutamic acid) (PLG), porous membrane actuators termed PLL-PMIM-Tf2N/PAA or PLL-PMIM-Tf2N/PLG, respectively, were tailor-made. Hemolytic tests support excellent blood cell compatibility of the fully polypeptide-based PLL-PMIM-Tf2N/PLG actuator. The as-made soft actuators could bend significantly up to 500°with a maximum curvature of 7 cm−1 in response to solvent vapor in a fast actuation process within 2 s. Their high sensitivity towards solvent molecules equips them with skills to distinguish solvent isomers, as exemplified by butanol isomers, in terms of bending curvature due to varied molecular interactions between the actuator and the isomer. To be highlighted is an unusual irreversible actuated tubular state of the fully polypeptide-based PLL-PMIM-Tf2N/PLG actuator that is stable in shape and resembles bionic blood vessels. Such polypeptide-type poly(ionic liquid) actuators are of significant value in future development of biocompatible devices for medical and healthcare applications.
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